cognomen vs byname

cognomen and byname both are nouns.

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

As nouns, cognomen and byname are synonyms defined as:

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

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

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