family name vs cognomen

family name and cognomen both are nouns.

Word	Noun	Adjective	Verb	Adverb
family name	Yes	No	No	No
cognomen	Yes	No	No	No

As nouns, family name and cognomen are synonyms defined as:

family name and cognomen: the name used to identify the members of a family (as distinguished from each member's given name)

Other synonyms of family name include last name, surname.

family name (noun)	cognomen (noun)
the name used to identify the members of a family (as distinguished from each member's given name)	the name used to identify the members of a family (as distinguished from each member's given name)
	a familiar name for a person (often a shortened version of a person's given name)