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Family name Stoy (Stoy , ستوي) , in all the world, is quite a rare last name. The surname Stoy is habitual in Isle of Man, where it is quite a rare surname, Germany, and Israel, where it is a rare surname. In absolute terms, this name is the most popular in the United States, Germany, and Israel. Very seldom, Stoy is the forename as well as the last name.