Word meaning "from which the name derives?"?

Question

There is an adjective for this - not nominal, not archtypical... as in, X word was originally invented to describe Y.
"Y, the ___ X."
"Calcutta, the ___ "black hole"
"Manchukuo, the ___ "puppet state"

Thanks!

Answer 1

I think the word you're looking for may be "eponymous".

Answer 2

I think you mean stereotypical, or maybe just typical. You usually use "a" and not "the" with typical though.

Answer 3

Perhaps an epithet.