surname vs cognomen

surname and cognomen both are nouns.

Word	Noun	Adjective	Verb	Adverb
surname	Yes	No	No	No
cognomen	Yes	No	No	No

As nouns, surname and cognomen are synonyms defined as:

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

Other synonyms of surname include family name, last name.

surname (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)