A "Kähler manifold" exists, as a name, because there is no way to fully describe what it is (and bring forward in the reader all the corresponding context) in two or three words. Using a long sentence (full of things that could themselves be artificial labels, recursively) instead would be a waste of everyone's time.
If one can use a short descriptive name for something, then it's not a name, it's just the thing, and everyone refer to it directly. And when you can't, or when you want to indicate its importance, or you want to neatly package all the relevant context about it, all the mathematical baggage that should come with it in something short, then the pretty obvious thing to do it to abstract it away and stick a label on top.
It doesn't really matter whether they use mathematicians, flower names or characters from The Lord of The Rings, as long as it's unique enough, in context, then it's fine. The names become part of the vocabulary of the field, just as much as supposed "descriptive" names. All those "descriptive" names have to be precisely defined too anyway, because they carry natural-language connotations, assumptions, and so on, that just don't apply.