The typical Roman had three names: the praenōmen (first name), the nōmen (gēns name), and the cōgnōmen (family name).
Mārcus Tullius Cicerō =
Mārcus (what’s up, Marcus?) +
Tullius (the time-honored descendants of Servius Tullius, 6th kind of Rome)
Cicero (the Cicero family, descended from some particular Tullian who earned the nickname ‘chickpea’)
A gēns is much larger than a family, and a Roman was more formally and less intimately attached to the name. ‘Mārcus Tullius Cicerō‘ may be compared to todays ‘John Proper III, descendant of James Black, Duke of York.’
On the day-to-day, he was just Mārcus Cicerō
When two members of the same family are mentioned together, the cōgnōmen is plural: Pūblius et Servius Sullae
What About Women?
No first names–no praenōmina, and no family names–no cōgnōmina.
Cicero’s daughter was Tullia
Further daughters would have been Tullia secunda, Tullia tertia, etc.
The Essential AG: 108, 108b
Famous Phrase: nōmen est ōmen : the name is a sign