writer's name vs author's name

writer's name and author's name both are nouns.

Word	Noun	Adjective	Verb	Adverb
writer's name	Yes	No	No	No
author's name	Yes	No	No	No

As nouns, writer's name and author's name are synonyms defined as:

writer's name and author's name: the name that appears on the by-line to identify the author of a work

writer's name (noun)	author's name (noun)
the name that appears on the by-line to identify the author of a work	the name that appears on the by-line to identify the author of a work