Roman male names are usually composed of three elements, as in “Gaius Julius Caesar.” In this case, Gaius (the praenomen) was his personal name, Julius (the nomen) the name of his gens (clan, or extended family), and Caesar (the cognomen) was a nickname, to distinguish him from all the other Gaii of the Julian clan. Originally cognomina were unique to the individual, but they quickly became hereditary, designating a particular family within the gens. I tell my students that a rough equivalent would be someone named “John MacTavish of Kintyre” – a John, member of clan MacTavish, residing in Kintyre (as opposed to any MacTavishes living in Arran, Islay, or Mull). The hereditary nature of the cognomen perhaps gave rise to a fourth element, the agnomen, a name that also designated a particular individual, as in Publius Cornelius Scipio Africanus (although agnomina could also become hereditary, or be reused, particularly when they designated victory titles like Africanus, Germanicus, or Britannicus).
Some people never took cognomina, such as Titus Livius (Livy) or Gaius Marius (Marius).
It seems that most Romans are known in English by English versions of their nomina:
Publius Virgilius Maro – Virgil
Publius Ovidius Naso – Ovid
Gauis Suetonius Tranquillus – Suetonius
Tiberius Claudius Caesar – Claudius
Quintus Horatius Flaccus – Horace
However, some names are derived from cognomina, e.g. (and see below):
Publius Cornelius Tacitus – Tacitus
Marcus Porcius Cato – Cato (the Elder)
Lucius Cornelius Sulla Felix – Sulla
Marcus Junius Brutus – Brutus
Gaius Julius Caesar – Caesar
At least one is derived from a praenomen:
Tiberius Julius Caesar – Tiberius
And another from an agnomen:
Gaius Julius Caesar Augustus – Augustus
What got me thinking about this whole issue was the number of Romans known in English by -ian names, such as:
Octavian, Vespasian, Domitian, Hadrian, Gordian, Valerian, Julian, Diocletian, Jovian, or Justinian
These of course are shortened from -ianus; Octavian was known as Octavianus in Latin. All of these, apparently, were cognomina. From an article on “Roman Naming Conventions”:
Some males had a cognomen that ends in –anus, which was adapted from and commemorated a nomen, sometimes their maternal family or—if they were adopted—their original paternal family. For instance, Vespasian’s nomen (Flavius) came from his father’s nomen. His cognomen (Vespasianus), on the other hand, was derived from his mother’s nomen, Vespasia. Others had cognomina that were derived not from the nomen, but the cognomen of their mothers’ families. For instance, Caracalla’s maternal grandfather was Julius Bassianus, but Caracalla’s cognomen was not Julianus, but rather Bassianus as well.
And Octavian only became Octavian when he was adopted posthumously by Julius Caesar. Born Gaius Octavius Thurinus, he became Gaius Julius Caesar in 44 BC, but known as Octavianus in honor of his birth nomen, and to distinguish him from his adoptive father.