What term refers to a family name indicating gens or clan in ancient Rome?

The correct term indicating a family name that represents a gens or clan in ancient Rome is nomen. In Roman naming conventions, a full name typically consists of three parts: the praenomen (given name), the nomen (indicating the gens or clan), and the cognomen (which often distinguishes between different branches within a clan). The nomen plays a critical role in identifying a person's familial connections and their standing within society, as it ties them to a specific lineage.

In contrast, cognomen is a surname that often indicated an individual’s personal characteristics or achievements and distinguished them from others within the same gens. Agnomen refers to an additional name, often assigned later in life for various reasons, such as honorifics or to commemorate an ancestor. Familia, while it refers to a household or family unit, does not specifically denote a clan or gens in the same way nomen does.