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Family name Doster (Doster , Достер , 多斯特) , worldwide, is quite a common cognomen. The family name Doster is characteristic of the United States, where it is quite a rare surname, Germany, where it is a rare surname, and Israel. Not in comparison with a country's population, it is commonest in the United States, Germany, and Turkey. Very seldom, Doster is the forename as well as the last name.