cognomen vs surname

cognomen and surname both are nouns.

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

As nouns, cognomen and surname are synonyms defined as:

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

Other synonyms of cognomen include family name, last name.

cognomen (noun)	surname (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)