There are indications that in the ancient times Romans possessed only one name like the most Indo-European peoples. By the Republican period of the Roman history, a stable naming system, called „tria nomina“ developed and was actively used. The full name consisted of a praenomen, a nomen gentilicium and a cognomen.
For girls on the eighth day after birth and for boys on the ninth, the praenomen was given formally, though, according to the custom of Quintus Mucius Scaevola the official listing of the name of the girl would only occur on the day of her marriage and for the boy on the day of assumption of the toga virilis, at the age of 16-17. 
The Roman praenomina must have once been very numerous. However, it was gradually reduced to 15-20. The reduction of the number of praenomina occurred likewise in Etruria. According to Michael Mitterauer two reasons have led to such a phenomenon: the growing importance of nomina gentilicia and concentration on several theophoric names that were to protect their bearers and express their religious beliefs.
Two most often encountered Roman praenomina Marcus and Gaius are derived from the god Mars, the legendary father of the founders of Rome Romulus and Remus, and Gaea, the Earth Goddess. Tiberius comes from a sort of a deity, the Father Tiber.
Some praenomina are derived from circumstances of birth: Lucius (the light of day), Manius (morning), Posthumus (born after his father`s death), Gnaeus („born“, „birthmark“), Spurius (possibly used for bastards), Publius (growing up, coming of age – „pubes“, grown up), Numerius („numbered“), Caeso („cut“ from the mother, hence Caesarian operation), Agrippa („born feet first“).
By the time of Cicero (43 b.C.) abbreviations of the most wide spread forenames start to ciculate: M., G. (or C.), L., P., Gn. (or Cn.), M`., Ti., T., Ser.
So called „number names“ start with the fifth son in the family: Quintus and continue: Sextus, Septimus, Octavius, Nonus, Decimus.  However, a finnish philologist Olli Salomies questions the fact that „number names“ were used to number sons in the family. He emphasizes that since these names only start with Quintus, they might designate the month of the child`s birth.
Roman parents (it would be more correct to say fathers, because fathers were obliged to name their children) were limited to a great extent while choosing names for their sons. Particular praenomina were reserved for definite families, for example: Cornelian gens used mainly Gnaeus, Lucius, Publius, Marcus, Servius and Tiberius, Scipio stirps of the Cornelian gens selected three praenomina: Gnaeus, Lucius, Publius. The Domition gens used Gnaeus and Lucius, the Bibulia Gaius, Lucius and Marcus, the Fabia and Quintilia Caeso. The Claudia has Appius and Decimus, the Aemilia Mamercus. Therefore, praenomina can be considered a necessary addition of nomina gentilicia and should not be viewed as an equivalent of modern first names that identify a person in the family.
Going back to the earliest Latin inscription on the Praenestine Fibula („Manius me fecit Numerio“), Leonard Ashley and Michael Hanifin outline that nomina were the heart of the Roman naming system. Indeed, nomen was the component of name that was inherited, indicated the position of the gens in the state, ist antiquity and sometimes ist origin. Nomen was shared by all the members of the family and slaves. Sometimes nomina originated from personal names, for example Marcius derives from Marcus, Tullius from archaic Tullus. However, the most nomina gentilicia come from names of tribes. Romans initially derived from three groups of tribes, genera maiora Ramnes, Tities and Luceres. Within major tribes there were smaller clans (gentes), e. g. Julians and Servillians were gentes of the Luceres tribe, as Livy reports. Families were further divided into stirpes: thus Caesar was a branch of the Julian gens of the Luceres tribe. To the original founding tribes were added 30 plebeian tribes. Names for all Roman tribes were given by the sixth Roman King, Servius Tullius. To non-patricians he gave names derived from the four quarters of Rome in which they resided. To the quarters of Rome the King also added 26 rural areas outside of the city. As a result of the seige of Rome by the Etruscan King Lars Porsena at the beginning of the 6th century b.C., the 30 plebeian tribes were reduced to 20. The four urban tribes remained, their historical names are: Suburana, Esquilina, Collina, Pallatina. The 26 suburban districts became 16: Aemilia, Camilia, Cornelia, Fabia, Galeria, Horatia, Lemonia, Menemia, Papiria, Pollia, Popillia, Pupinia, Romilia, Sergia, Veturia and Voltinia. Later the Claudian gens was added to the 16 tribal names. More nomina were added in the 4th century b.C.: Stellatina, Tromentina, Sabatina and Arniensis, Pomptina, Publilia, Maecia, Scaptia, Ufentina, Falerina. In the 3d century b.C. more tribal names appeared: Aniensis, Terentina, Quirina and Velina.
Five leading families of the classical Rome were Claudia, Cornelia, Aemilia, Fabia and Valeria. Notable among the patricians were bearers of the following nomina: Julia, Junia, Porcia, Sempronia, Gracchi, Cassia, Licinia, Tullia, Horatia, Domitia, Manlia, Calpurnia, Flavia, Livia, Caecilia, Roscia, Marcia, Antonia. There also existed non-patrician nomina, that were equestrian or upper middle-class: Octavia, Pompeia, Vipsania. There is at least one famous nomen of a common origin: Marius.
Cognomina only appear in public documents at the time of Sulla. However, they must go back much farther, since a period of variations in the rules of the usage of cognomina could have been fairly long.
Charlotte M. Yonge gives the following definition of cognomina: „Roman cognomina were originally neither more nor less than nicknames, sometimes far from complimentary, but for the sake of convenience, or of honourable association, continued in the family.“ Ashley and Hanifin consider cognomina actual surnames. They note, that the most cognomina were originally agnomina, nicknames. They could derive from physical peculiarities: Rufus (red-head), Cincinnatus (with curly hair), Flaccus (flop-eared), Casca (the one who looked old), Celsus (tall), Barbatus (bearded), Chlorus (pale), Curtius (short), Caecus (blind), Crassus (fat), Lentulus (slow), Calvus (bald), Nasica (pointly-nosed), Niger (black), Longus (long, tall), Lepidus (lovely). Some cognomina arose from mental qualities: Maximus (best), Superbus (haughty), Antipater (against his father), Sophus (gr. „wise“), Cato (clever), Brutus (brutish). Some cognomina defined occupations: Curio (priest of the curia), Cursor (runner), Agricola (farmer), Mallius (an ironworker), Pictor (painter), Faber (carpenter). A cognomen could be taken from a totem: Lupus (wolf), Caepio (onion), Corvinus (raven), Lentulus (bean), Piso (pea), Cicero (vetch). Diminutives have been popular nicknames: Marcellus (little Marcus), Lucullus (little Lucius), Catullus (little clever one), Asellio (little donkey). Cognomina could also indicate the birthplace of the forefather: Hadrianus, Albinus. Sometimes distinguished personages were granted cognomina in memory of their services: Coriolanus, Capitolinus, Africanus, Asiaticus, Narboniensis, Salonius, Britannicus. It is interesting that a father could leave his cognomen to only some of his sons.
A fair number of Etruscan cognomina was preserved: Caecina, Perperna, Sisenna, Spurinna, Aulinea, Largenna, Mastarna, Porsenna, Saserna, Velina, Vibenna.
Honorific additions, such as Censor, Consul, Praetor, Aedile, were so-called cognomina ex virtute. They usually were used only during term of office.
We already mentioned that Roman families were limited while choosing praenomina for their children. Surprisingly, in case of cognomina there existed similar limitations. Certain patrician families selected a few cognomina, that were carried by further generations. For example, the gens Aemilia only used the following cognomina: Barbula, Buca, Lepidus, Mamercus, Papus, Paullus, Regilus and Scaurus. The patrician line of the gens Claudia used Caudex, Centho, Crassus, Nero, Pulcher, Regillensis and Sabinus. The plebeian Claudii called themselves Asellus, Canina, Centumalus, Cicero, Flamen and Marcellus. The Julia gens involved Caesar, Libo and Mento. The Valeria gens used Barbatus, Catullus, Corvus, Falto, Flaccus, Laevinus, Maximus, Messala, Potitus, Publicola, Tappo, Triarius and Volusus.
Adoption was popular in some ancient cultures, but only under Greeks and Romans it achieved the scale of habitual usage. It was immensely important for a Roman family to continue its male line, to have a male heir. It might seem peculiar to us that oftentimes adults were adopted, furthermore, their natural parents might be alive. Natural parents allowed their sons to be adopted due to the distinction of the adopters, besides, if a father had several sons, he could afford „loaning“ one or two to a childless family. For example, one of the personages of this site, Aemilius Paullus let two of his sons from the first marriage be adopted: one by Africanus and the other by Quintus Fabius Maximus, becoming Quintus Fabius Maximus Aemilianus. Unfortunately, after his two older sons had been adopted, his two younger ones died at the age of 12 and 15.
The adopted child kept the nomen of the true father (with the suffix –ianus) as an agnomen and changed his praenomen nomen and cognomen to those of the adopter. Thus, Gnaeus Octavius, adopted by Gaius Julius Caesar, became Gaius Julius Caesar Octavianus. Later he added the famous agnomen Augustus to his name.
The most scholars do not bother to dedicate more than a paragraph to female Roman names. Thus, Miguel Dolç is writing, „The system of female names was more primitive and less stable compared to male names according to the minor role Roman women played in the society. Usually women did not have a praenomen. The name of an unmarried woman cosisted of her family`s nomen and her father`s praenomen: Cumia L. f. Oftentimes the nomen was followed by a cognomen with a suffix –illa or –ina: Livia Drusilla, the second wiffe of Augustus, was a daughter of M. Livius Drusus Claudianus; Valeria Messalina, the first wife of Claudius, was a daughter of Valerius Messalla. Younger daughters received a name-number: Secunda, Tertia, Quarta. Upon getting married, a woman added the name of her husband to her name: Pupilia Turpilia Cn. Uxor“.
Textbooks on Roman epigraphy usually contain information that in pre-republican Rome women bore individual names. Ernst Meyer assumes that there were many personal female names.
According to the legend of seizure of the Sabine women by Aeneas, the names of areas around Latium imitate the names of Sabine women and correspond to some Roman nomina: Aurelia, Cornelia, Lucretia. These names can be roughly considered the earliest examples of Latin female names.
Some families added a cognomen to the names of their women. For example, Caecilia gens had a custom of giving the name Caecilia Metella to all its female members. Starting from the time of Sulla cognomina could be used for distinction of different branches of a family. It was reflected in the names of women, which now could include the cognomen of the father. Sometimes the mother`s name was added to the full name of a woman.
Some researchers of Roman names, Iiro Kajanto among them, think that in the late Roman Republic personal informal female names could be used in the family, such as Paulla (little). During the early imperial period individual names start to circulate. In the documents they were placed after nomina.
Officially Roman women did not belong to themselves, they necessarily had a curator which was the father in case of an unmarried girl or the husband in case of a married woman. If the woman lost both the father and the husband, a male relative became a curator. Only the reforms of Augustus allowed the mothers of three children (four for female slaves) to run the household independently. It is therefore obvious, why women were „named“ after the father and the husband.
There is a curious Roman marriage custom: at the end of the ceremony the bride arrived to the house of the groom, who waited for her at the threshold. The groom asked the bride to tell her name and the girl answered, „Where thou art Gaius, I am Gaia“. She then was carried over his threshold, to prevent the ill omen of touching it with her feet. From this rite all girls were called Gaiae.
Usually it is noted that even after marriage the woman preserved the nomen of her father and did not gain one of her husbands. Furthermore, women were buried with their fathers and even after marriage nominally belonged to the family of their fathers. Nevertheless, it should be remembered that two types of Roman marriage existed. If the marriage in manus took place, the woman entered the family of her husband and officially became a daughter of the new pater familias. In case of marriage sine manu the woman did not lose connection to her own family. Such marriages started to be stipulated in the 3d century b.C. and by the 1st century a.D. they became quite popular.
Slaves took their names from that of the master. For example, Marcipuer and Marcipuella from Marcus. When slaves were freed, they dropped the derivative of their master`s name and acquired the master`s praenomen and nomen. Sometimes they also added to their full name a latinized version of their original name (which was usually foreign). The same occurred when a foreigner was granted the Roman citizenship, only he was supposed to assume the name of the emperor under whose rule the citizenship was granted.
Starting from the 1st and 2d centuries a.D. clear tendencies of the instability of the tria nomina system can be observed.
1. The mother line of the family becomes important, thus contributing more names to chose from. Chidren could receive the praenomen of the father as well as praenomina from the mother`s side of the family, nomina and cognomina of the father and the mother were written down one after another, sometimes without any order whatsoever. The number of components of a name could reach several dozens. A famous Consul of the year 169 was called Q. Pompeius Senecio Roscius Murena Coelius Sex. Julius Frontinus Silius Decianus Caius Julius Eurycles Herculanus L. Vibullius Pius Augustanus Alpinus Bellicius Sollers Julius Aper Ducenius Proculus Rutilianus Rufinus Silius Valens Valerius Niger Cl. Fuscus Saxa Amyntianus Sosius Priscus. This name has 38 components!
2. More and more foreigners were granted Roman citizenship. Following the Roman tradition all the new citizens were obliged to add the name of the emperor-benefactor to their names. Thus, in the 3d century a.D. one fifth of all the nomina in Rome were imperial. In the index of the Corpus Inscriptionum Latinarum Aelius occupies 22 columns, Aurelius 34, Claudius 33, Cocceius 4, Flavius 28, Julius 45, Septimius 4 and Ulpius 16. The nomen Aurelius must have been the most wide spread. In the year 212 the Aurelian Caracalla granted all the free inhabitants of the Empire the Roman citizenship with the Constitutio Antoniana. All these people automatically assumed the name of the emperor. Obviously the meaning of the nomen gentilicium was lost.
From the 3d century a.D. Christian nomina singularia are used more and more often. Praenomina and nomina are at first abbreviated, then they are dropped and finally only cognomina are left. However, names that consisted of two or three elements continued to be used up to the 5th - 6th centuries a.D. According to the statistics of Iiro Kajanto, nomina singularia made 96,3 % in the 6th century a.D. in case of male names and 98 % in case of female names.
 Ashley Leonard, Hanifin Michael, 1978, P. 340
 Mitterauer Michael, 1993, P. 78.
 Ashley Leonard, Hanifin Michael, 1978, P. 349-345
 Ashley Leonard, Hanifin Michael, 1978, P. 343
 Ashley Leonard, Hanifin Michael, 1978, P. 306
 Yonge Charlotte M., 1863, P. 303
 Ashley Leonard, Hanifin Michael, 1978, P. 306-312
 Ashley Leonard, Hanifin Michael, 1978, P. 312-315
 Yonge, Charlotte M., 1863, P. 330
 Ashley Leonard, Hanifin Michael, 1978, P. 3268-369
 Ashley Leonard, Hanifin Michael, 1978, P. 374
 Dolç, Miguel, 1960, P. 390
 Meyer, Ernst, 1973, P. 89
 Kajanto, Iiro, 1987, P. 59
 Yonge, Charlotte M., 1863, P. 285
 Dolç, Miguel, 1960, P. 400
 Mitterauer, Michael, 1993, P. 84