You do see definite articles used in a lot of such cases, though... The Matterhorn, The Zugspitze, The Grand Canyon, The Dead Sea, The Arctic Ocean, The Gulf of Oman... any one of those would sound wrong without the "The" in front of it, in most normal contexts. "The Kékes" feels like it's in the same category to me, and that's how I would refer to it aloud in English.
The main problem is that the above Hungarian question - "Mi van a Kékestetőn?" - is wrong, it doesn't make sense, because Kékestető is a village. "What is on a/the village?" it is completely pointless, this causes the confusion. You have to report the Hungarian version of the above question, not the English one.
I think the most natural way to say this in English is "What is at the top/peak of Kékes?" "On top of" describes a spatial relationship, but that's obvious when talking about a village on the peak of a mountain. To me it sounds a little silly to say that the village is "on top of" the peak. Yes, we knew that - where else would it be? Underneath the peak? :) "At the peak" implies on top of it, IMO.