In his memoir "The Black Dog of Fate" Peter Balakian gives a breakdown like this for a relative branch of the family named Shekerlemejian: "şeker" is Turkish for "sugar" and "şekerleme" is "things made with sugar" so a candy seller got an occupational name and then their child got the patronymic form.

All of this to say: there's an n=1 elsewhere for this happening to Ottoman Armenians.