I'm surprised you understand the word "eponymous" so clearly. When I hear it I get confused. The dictionaries show some wide discrepancies in meanings. What I mean is that some define the words "eponymous" and "eponym" as either being from source to derived, derived to source, or both ways.
Meaning being the origin after which something is named:
adjective
: of, relating to, or being the person or thing for whom or which
something is named :
Merriam-Webster Dictionary
adjective
giving one's name to a tribe, place, etc.: Romulus, the
eponymous founder of Rome.
Random House Kernerman Webster's College Dictionary
The other way:
2.Named after something else or deriving from an existing name or word:
American Heritage Dictionary
Going both ways:
eponymous
adjective
1(of a person) giving their name to something.
1.1 (of a thing) named after a particular person or group.
Oxord Living Dictionaries
1.(of a person) being the person after whom a literary work, film, etc, is named:
2.(of a literary work, film, etc) named after its central character or creator:
Collins Dictionary
In addition to this, some dictionaries define eponymous as:
1.Of, relating to, or constituting an eponym.
American Heritage Dictionary
So we can look up "eponym" and see if we see the same discrepancies that we have with "eponymous".
"eponym"
n.
1. A word or name derived from a proper noun. The words atlas, bowdlerize, denim, and Turing machine are eponyms.
2. One whose name is or is thought to be the source of the name of something:
American Heritage Dictionary
American Heritage Dictionary tells us that an eponym goes both ways.
n
1. a name, esp a place name, derived from the name of a real or mythical person, as for example Constantinople from Constantine I
2. the name of the person from which such a name is derived:
Collins Dictionary
Collins says "eponym" can go both ways.
n.
1. a person, real or imaginary, from whom something takes or is said to take its name.
2. a word based on or derived from a person's name.
Random House Kernerman Webster's College Dictionary
The above says "eponym" can go both ways.
1 : one for whom or which something is or is believed to be named
2 : a name (as of a drug or a disease) based on or derived from an
eponym
Merriam-Webster Dictionary
Merriam-Webster Dictionary, in its wisdom, uses the word it's defining in the definition itself. However if we take "eponym" in definition (2) to have the meaning from definition (1), then Merriam-Webster also says it can go both ways.
Cambridge Dictionary gives us what I find to be the most unclear definition.
eponym
noun
the name of an object or activity that is also the
name of the person who first produced the object or did the
activity
Cambridge Dictionary
The above meaning seems to go only one way.
Here is what Wikipedia has in its "eponym" article.
An eponym is a person, place, or thing after whom or after which
something is named, or believed to be named. For example, Elizabeth I
of England is the eponym of the Elizabethan era, and "the eponymous
founder of the Ford Motor Company" refers to Henry Ford.
So this says that "eponym" is the source for or after which others are named. However it then gives a meaning which goes the opposite way:
Recent usage, especially in the recorded-music industry, also allows
eponymous to mean "named after its central character or creator".
Eponym Wikipedia article
Grammarist website has a short article about the use of "eponymous", and it makes the same point made in the Wikipedia article about its recent use.
By the way, the same discrepancies in meaning are found among dictionaries with the word "namesake".
In addition to all these different definitions, also keep in mind that some definitions only mention "people" or "titles" (films, books), while others are more extensive or all-encompassing, that is, they mention placenames, and things in general, like objects, activities etc.
You can make of all this information what you want. I for one am really confused. One general thing I've noticed is that "eponym" is defined to mean both ways, whereas for "eponymous" this is less common. If you assume "eponymous" to mean "relating to or constituting an eponym", which I only found in one dictionary, then you can see that most dictionaries define "eponym" in both ways, that is, from source to derived and the opposite way.
Whether or not using it like this:
Prince Hamlet is the main protagonist in Shakespeare's eponymous play.
... will confuse people, or be frowned upon, I'm not sure. The fact that I find it confusing is probably a quirk of mine.
A Google search for "eponymous play" gets 18,400 results (though be careful, maybe something has been named after the play), and seem to be from reputable sources:
Macbeth
Shakespeare Survey: Volume 63, Shakespeare's English Histories and Their Afterlives
1 Henry IV: A Critical Guide
A Companion to Sophocles
Clicking these links will bring you to the use of "eponymous play".