Meronym

The -onym part is from a Greek root for "name"; it's where we get "synonym", "homonym" and so forth.   I'm not familiar with "meronym" nor with the "mero-" part.   Let's look it up...yep, μέρος and μερίς both mean "part".   Two years of college Greek and I still don't know that one!

"Mytonymy" I don't know either.   When I look that up, "mytonymy" doesn't appear and I see that the "myto-" prefix isn't in English at all; "mytologia" is Finnish and "mytologie" is Czech, both for "mythology".   But I thought "metonymy" sounded familiar, and once I looked that up I'm sure it's what you meant; it's from Greek μετά+ὄνομα ("changing the name", sort of).

Then I looked up "synecdoche".   Three words in one post I was almost completely ignorant of; I knew I'd seen "synecdoche" before, but wouldn't have been able to tell you what it means.   According to the dictionary I found, synecdoche is referring to a part when you mean the whole, or vice versa; metonymy is when you mean one thing and refer to something closely related to it.   So I would judge that synecdoche is a subset of metonymy.

So is there any discernible difference between a meronym and a metonym?   Well, this is all new territory to me, but what I see here is that a meronym is a word that refers to a part of something in order to mean the whole (in the phrase "20 head" (of cattle), "head" is a meronym for "cow"), and a metonym is a word that's used to mean a thing it's related to (eg "Jerusalem" can be used to mean the Israeli government).   There's a lot of overlap there, but they aren't exactly the same.

Yes, I've wrote it that way (mytonomy) several other times recently. A recent phenomenon.:-D

It's metonymy.

Yes, of course, I meant I did that by mistake.