Do you have to provide the author’s name in a parenthetical citation for a work of common literature such as The Iliad?

Note: This post relates to content in the eighth edition of the MLA Handbook. For up-to-date guidance, see the ninth edition of the MLA Handbook.

Yes, unless you have already mentioned the author’s name in your prose. Just because a work is famous doesn’t mean you can omit the name of its author.