Roman names were a complicated affair. Roman males were generally given 3 names, a praenomen, a nomen gentilicum, and a cognomen.
For males the praenomen or first name was usually chosen from among fourteen common names. Thus there were innumerable men with the name Antony, Publius, Marcus, Lucius or Titus. Because of the common nature of these names they were often abbreviated and seldom used to refer to a specific person.
The middle name, nomen gentilicum, was the family name, much as we think of surnames today. Thus a name like Gaius Julius Caesar would denote a member of the Julian clan. This name, in a modified form was also given to any female born into the family. So sisters would all have the same name. Gaius Julius Caesar's daughter was named Julia. The woman would then take on the nomen gentilicum of their husbands. Thus, when Julia married Gnaeus Pompeius Magnus, she became Julia Pompei.
Finally, the cognomen was a nickname that indicated some personal aspect of appearance or personality. It was usually a name held only by a specific person and distinguished them from the rest of the male Roman population. Thus the famous orator Marcus Tullius Cicero was known primarily by his cognomen which meant "chick pea".
Interesting Link: Gaius Valerius Catullus