Ancient Greek Names:
In literature, ancient Greeks are usually identified by only one name -- whether male (e.g., Socrates) or female (e.g., Thais). In Athens, it became mandatory in 403/2 B.C. to use the demotic (the name of their deme [See Cleisthenes and the 10 Tribes]) in addition to the regular name on official records. It was also common to use an adjective to show place of origin when abroad. In English we see this in such names as Solon of Athens or Aspasia of Miletus [see Miletus on map].
Ancient Roman Names:
During the Republic, literary references to upper class men would include the praenomen and either the cognomen or the nomen (gentilicum) (or both -- making the tria nomina). The cognomen, like the nomen was usually hereditary. This meant there could be two family names to inherit. The statesman M. Tullius Cicero is now referred to by his cognomen Cicero. Cicero's nomen was Tullius. His praenomen was Marcus, which would be abbreviated M. The choice, while not officially limited, tended to be among only 17 different praenomina. Cicero's brother was Qunitus Tullius Cicero or Q. Tullius Cicero; their cousin, Lucius Tullius Cicero.
Salway argues the 3 name or tria nomina of the Romans is not necessarily the typical Roman name, but is typical of the best documented class in one of the best documented periods of Roman history (Republic to early Empire). Much earlier, Romulus was known by a single name and there was a period of two names.
By the first century B.C. women and the lower classes began to have cognomina (pl. cognomen). These were not inherited names, but personal ones, which began to take the place of the praenomina (pl. praenomen). These might come from part of the woman's father's or mother's name. By the 3rd century A.D., the praenomen was abandoned. The basic name became the nomen + cognomen. Alexander Severus' wife's name was Gnaea Seia Herennia Sallustia Barbia Orbiana.
See J.P.V.D. Balsdon, Roman Women: Their History and Habits; 1962.
There were two other categories of names that might be used, especially on funerary inscriptions (see accompanying illustrations of an epitaph and a monument to Titus), following the praenomen and nomen. These were the names of filiation and of tribe.
A man might be known by his father and even his grandfather's names. These would follow the nomen and be abbreviated. The name of M. Tullius Cicero could be written as "M. Tullius M. f. Cicero showing that his father was also named Marcus. The "f" stands for filius (son). A freedman would use an "l" for libertus (freedman) instead of an "f".
After the filiation name, the tribal name could be included. The tribe or tribus was the voting district. This tribal name would be abbreviated by its first the letters. The full name of Cicero, from the tribe of Cornelia, would, therefore, be M. Tullius M. f. Cor. Cicero.
"What's in a Name? A Survey of Roman Onomastic Practice from c. 700 B.C. to A.D. 700," by Benet Salway; The Journal of Roman Studies, (1994), pp. 124-145.
"Names and Identities: Onomastics and Prosopography," by Olli Salomies, Epigraphic Evidence, edited by John Bodel.