In the naming convention of ancient Rome the archetypical name of a male citizen consisted of three parts (tria nomina): praenomen (given name), nomen gentile or gentilicium (name of the gens or clan) and cognomen (name of a family line within the gens). Sometimes a second or third cognomen, called agnomen, was added. This system was derived from the Etruscan civilization.
Females were officially known by the feminine form of their father's nomen gentile, followed by the genitive case of their father's cognomen (husband's if married), and an indication of order among sisters. By the late Roman Republic, women sometimes also adopted the feminine of their father's cognomen.

History
The praenomen (literally forename) was the only name in which parents had some choice, roughly equivalent to the given name of today. It was a personal appellation given to an infant on their day of lustration. As a rule only the immediate family would call a person by his praenomen. Compared to most cultures, Romans used very few different praenomina: the common praenomina were fewer than 40, and about 18 in the late Republic. Some gentes used only a few of these praenomina, and some of the praenomina in turn were used only in one gens. The Cornelii, for example, rarely named their sons anything other than Gnaeus, Lucius, and Publius. The pater familias often named infants after himself, in masculine or feminine form (Lucius, Lucia). Most praenomina are masculine o-stem (nominative in -us) or feminine a-stem nouns.
A study of praenomina found in the Corpus Inscriptionum Latinarum shows that the seventeen most common male praenomina accounted for 98% of all male roman names. The most popular, Lucius, Gaius, and Marcus, constituted 59% of the total. In the 3rd century the nomen gentilicium Aurelius became one of the most popular praenomina after the emperor Marcus Aurelius Antoninus (Caracalla) granted universal Roman citizenship to all freeborn subjects throughout the Empire as new citizens adopted the name of their emperor in gratitude.
Senatorial decrees outlawing certain families from using certain praenomina was a Roman tradition. Livy relates how in the 4th century BCE Marcus Manlius Capitolinus was tried and condemned for treason. It was decreed that no member of the Manlia gens might thereafter bear the praenomen of "Marcus" which none did until the 1st century CE.
Many of the praenomina used by male citizens were abbreviated to one or two characters in writing or inscriptions; the more common abbreviations include: Appius (Ap.), Aulus (A.), Flavius (Fl.), Gaius (C.), Gnaeus (Cn.), Decimus (D.) Lucius (L.), Manius (M'.), Marcus (M.), Publius (P.), Quintus (Q.) Servius (Ser.), Sextus (Sex.), Spurius (Sp.), Titus (T.), Tiberius (Ti.). The names Primus, Secundus, Tertius, Quartus, Quintus, Sextus, Septimus, Octavius, Nonius, and Decimus mean, respectively, 'first', 'second', 'third', 'fourth', 'fifth', 'sixth', 'seventh', 'eighth', 'ninth', and 'tenth', and were originally given to first, second, third, etc. sons in birth order. There are, however, abundant examples of this birth-number significance being later lost: Sextus Pompeius, for instance, was not a sixth son. A possible explanation for this is that the numerical praenomen came instead to stand for the number of the month in which the person was born . Another explanation is that eventually parents thought the names were euphonic, and names such as Decimus no longer had to be the tenth child or born in December, and had become common names.

Praenomen
See also: list of Roman nomina
The second name, or nomen gentile, is the name of the gens (the family clan), in masculine form for men. The original gentes were descended from the family groups that settled Rome. These eventually developed into entire clans, which covered specific geographic regions. As the area of Rome expanded the number of tribes also expanded, so that not all tribes were from original settlers. Some were named for Etruscan families, while others were from local tribes or from major geographical features, such as rivers. Well-known nomina include many of the familiar names of ancient Rome, such as Aemilius, Claudius, Cornelius, Domitius, Julius, Pompeius, Antonius and Valerius.

Nomen gentile or Gentilicium
See also: list of Roman cognomina
The third name, or cognomen, began as a nickname or personal name that distinguished individuals within a gens. Cognomina do not appear in official documents until around 100 BC. During the Roman Republic and Empire, the cognomen is inherited from father to son, serving to distinguish a family within a gens. Often the cognomen was chosen based on some physical or personality trait, sometimes with ironic results: Julius Caesar's cognomen meant hairy (cf. etymology of the name of Julius Caesar) although he was balding, and Tacitus's cognomen meant silent, while he was a well-known orator.

Cognomen
A second cognomen (called agnomen) was sometimes added to make a distinction within a family. Most were used as nicknames, but some were inherited like the cognomen, thus establishing a sub-family. Some examples are found in List of Imperial Roman victory titles.

Agnomen
Adoption in Rome was common since most families had few children. When a man was adopted into another family, his name would become the adopted father's full name, plus a cognomen identifying his birth family. Examples from Roman history:

Publius Cornelius Scipio Aemilianus Africanus, the biological son of Lucius Aemilius Paullus Macedonicus, adopted into the family Cornelius Scipio.
Mamercus Aemilius Lepidus Livianus (Princeps senatus, 1st century BC), born as the son of a Livius, adopted into Aemilii Lepidi. Foreign names
There is written evidence that in the earliest period, praenomina had female versions and that women's names presumably consisted of a praenomen and nomen gentile, followed by filiation.
But by the time of the historically attested Republic, women no longer normally had praenomina. Instead, they were officially known only by the feminine form of their father's nomen gentile so that daughters were all named with the same feminine version of the family nomen. If further description was needed, the name was followed by the genitive case of her father's cognomen or, after marriage, of her husband's. Hence, Cicero speaks of a woman as Annia P. Anni senatoris filia (Annia the daughter of P. Annius the senator).
If only two daughters survived, they could be distinguished as major and minor. Marcus Antonius's daughters were Antonia major (grandmother of the emperor Nero) and Antonia minor (mother of the emperor Claudius). If a family had more than two daughters, they were distinguished by ordinal numbers: Cornelia Quinta, the fifth daughter of a Cornelius.
By the late Republic, women also adopted the feminine form of their father's cognomen (e.g., Caecilia Metella Crassi, daughter of Q. Caecilius Metellus and wife of P. Licinius Crassus). This feminized cognomen was often made a diminutive (e.g. Augustus's wife Livia Drusilla was the daughter of a M. Livius Drusus).
There are some examples where a woman took her mother's name: Arria was a daughter of Thrasea Paetus and his wife Arria (Tac. Ann. 16, 34; Pliny Ep. 3, 6, 10; 7, 19, 3); and possibly Considia, daughter of Servilius Nonianus (Pliny NH 24, 43), based on an assumption by Syme (Syme; 1964a:412f).

Female names

Additional elements and examples
In earlier Roman names, the praenomen and nomen gentile constituted a Roman's full name and were followed by the so-called filiation (a patronymic or indication of paternity). The filiation (patronimicus) consisted of the Latin word for "son" filius (abbreviated by the letter f.) preceded by the abbreviation of the father's praenomen, which was understood in the genitive. Hence, a Roman might have been known as M. Antonius M. f. (Marci filius), that is, Marcus Antonius, son of Marcus. Additionally it could also indicate the grandfather with the word "grandson" nepos (abbreviated by the letter n.).
By the Middle Republic, the abbreviation for tribe in which the man was enrolled was added after his filiation. When this became an official part of the name is not known.

Filiation
A tribe was a geographic distinction, not an indication of ancestry. A man belonged to the tribe in which his main residence was located. The tribe was an essential part of citizenship, since voting was often carried out by tribe. With the expansion of the Empire, the number of tribes also grew. See list of Roman tribes.

Tribes
Analysis of an example complete name: Marcus Aurelius Marci f. Quinti n. tribu Galeria Antoninus Pius, domo Caesaraugusta.
In everyday use, people were referred to by their cognomen, or praenomen plus nomen gentile. So, "Marcus Livius Drusus" would either be just "Drusus" or "Marcus Livius". "Iulia Marciana" would be just "Iulia". This has created problems for modern scholars, since in many cases we no longer have the contemporaneous context to know which person was actually meant.

praenomen: Marcus
nomen gentile: Aurelius (he belongs to gens Aurelia, the Aurelii in plural)
patronimicus: son of Marcus
grandparent: grandson of Quintus
tribe: Galeria (a tribe from the region of Caesaraugusta in Hispania)
cognomen: Antoninus (family of the Antonini)
agnomen: Pius (probably because of his piety... Rarely inherited)
city: Caesaraugusta (ancient Saragossa or Zaragoza in Hispania) Evolution of a personal name

Roman victory title
List of Roman praenomina
List of Roman nomina
List of Roman cognomina
List of Imperial Roman victory titles
List of Roman tribes
List of Roman female names
Roman Republic
Roman Empire