Does "eponymous" require that the compared things have the same name, or will a descriptor do?
Solution 1:
Whatever its traditional usage, today the word 'eponymous' is often used to indicate associations between the name of a thing and the origin of the name.
For example, consider this usage which is exactly backward from the traditional meaning yet exceedingly common: "Weezer's eponymous debut."
The strictest usage would be to limit it purely to actual names with the eponym being the one who yielded the name to the other thing. However, your dictionary sources suggest that it is common to stretch that to associations of title or unique descriptors that can also serve the function of a name in the context (as with The Little Mermaid and The Merchant of Venice).
Another case that you did not mention but which came to my mind while responding is 'the Count of Monte Cristo,' which is effectively the name of the character in the most of the book yet is not truly the character's name.
If you are concerned about being absolutely faithful to the roots, I would suggest sticking with cases where a person's name has turned into a label for something else, but I think you are safe to use it with characters like Ariel as well without seeming ignorant or sloppy. The case of the Weezer album is the only one I would say should be left out of writing that is expected to be fully proper, but I would probably tell a blogger about rock music that it okay to leave it in all the same as it's a common enough idiom.
Solution 2:
The word is of 19th century origin, constructed from Greek forms. If you want to stay literal to the original Greek meaning of -onym, then the Greek root word is ὄνομᾶ, and it means "name" not "reference." (A second sense is reputation, as in "make a name for oneself," but this does NOT mean "make a reference for oneself.") If you're interested, you can read the full definition of ὄνομᾶ from the LSJ at on the Perseus Ancient Greek word study tool and decide for yourself. :-) For me, I'll stick with the "name" sense and not the "reference" sense.
Solution 3:
I would say eponymous specifically means the person's name is used.
So the "Royal Shakespeare Company" is eponymous but the Globe Theatre isn't
Solution 4:
There's a lot of confusion: I remember when George Melly's autobiography Rum, Bum and Concertina came out, I read a review mentioning "his eponymous bum", which would certainly mean Antonio and Ariel qualify. But it's such a nice word to use I suspect that writers stretch the definition to fit it in.