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Family name Durst (Durst , Дурст , דורסט ) , all around the world, is a common cognomen. The cognomen Durst is characteristic of Western Europe, particularly Switzerland, where it is quite a common surname, Germany, where it is quite a rare surname, and Austria. Not in comparison with a country's population, it is commonest in the United States, Germany, and Switzerland. Very seldom, Durst is the forename as well as the last name.