Traditionally one’s complete name was of three parts:
Praenomen + Nomen + Cognomen.
For example, Gaius Julius Caesar:
Gaius was his prae (first) nomen, one of roughly 12 to 15 popular names that were almost exclusively used.
Julius was his tribal/family name. In this example he belongs to the family of the Julii, an ancient family name.
Caesar was his cognomen, a personal name or “nickname” that usually identified a personal characteristic, accomplishment or title. In this particular case “caesar “ meant hair or hairy. After his death, future emperors claimed “Caesar” as a title, thus “ruler.”
In The Peregrine's Odyssey, Gaius has the cognomen “Peregrinus” meaning wanderer. His nephew Marcus came to be known as Marcus “Africanus.”
These names identified one’s family lineage, place of birth, position, unique characteristics and/or accomplishments.