It also basically means ‘man’ or ‘person’:

From Old Hungarian mogyër. The first element (‘mogy-’) is likely from Proto-Ugric ‘*mańćɜ’ (“man, person”). The second element, ‘-ër’ (“man”), retained in ‘ember’ (“man”) and ‘férj’ (“husband”), from Proto-Uralic ‘*irkä’ or ‘*ürkä’ (“man, son, boy”).

So Hungarians were super lazy in the choice of the last names, not even picking the profession or patronymic, but just ‘man’.