Büki

There is a small town Bük near the Western border of Hungary (https://en.wikipedia.org/wiki/B%C3%BCk), so the name may refer to a person originating from there. Beech tree and the mountain name derived from it are both spelled with double 'k', which is usually kept when referring to the Bükk mountain as origin, i.e. bükki. E.g. Bükki Nemzeti Park = Bükk National Park.