"We travel to Kékes, and you?"
Translation:A Kékestetőre utazunk, és ti?
Why is this place sometimes called Kékestetőre, and sometimes just Kékes? Which is correct?
Both are correct. Officially, "Kékes" is the mountain itself, while "Kékestető" is the summit, and the official name of the "settlement". But the whole point of going to that mountain is usually to go to the top, so they may be used interchangeably. Besides, "Kékes" is the actual name part of the compound word, "tető" means "top" or "roof". So it is similar to saying "I am going to the Smoky Mountains" vs "I am going to the Smokies". Btw, "kékes" means "bluish".
Why does Duolingo use one name in English, and the other in Hungarian? Most place names in Hungary translate verbatim, and so far as I know this is included in that. (If you wanted to translate non-verbatim, the right word would be "peak", as in "Kékes peak".)