The word eponymous has to do what is named. Some examples are Lake Victoria, Faraday’s Laws, etc. The usage of the word eponym as a noun and eponymous as an adjective is a trifle confusing especially when you do not know the difference between what is named and the name itself.
Some examples of the word used in books:
“The screen blanked, then produced a book cover. The jacket image—in black-and-white—showed barking dogs surrounding a scarecrow. In the background, shoulders slumped in a posture of weariness or defeat (or both), was a hunter with a gun. The eponymous Cortland, probably.”
“Emma is the eponymous heroine, which means having the name that is used as the title or name of something else.)”
― Joan Elizabeth Klingel Ray, Jane Austen For Dummies