byname vs cognomen

byname and cognomen both are nouns.

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

As nouns, byname and cognomen are synonyms defined as:

byname and cognomen: a familiar name for a person (often a shortened version of a person's given name)

Other synonyms of byname include moniker, nickname, sobriquet, soubriquet.

byname (noun)	cognomen (noun)
a familiar name for a person (often a shortened version of a person'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)