Várkonyi is Hungarian surname:
Hildebrand Dezső Várkonyi (1888, Kéménd - 1971, Budapest), a monk and a teacher of Bencés order
Mátyás Várkonyi (born 1950), one of the most renowned musical composers in Hungary
Péter Várkonyi (1931–2008), a Hungarian politician
Robert Varkonyi (born 1961, New York), an American poker player
Michael (Mihály) Várkonyi, Hungarian actor