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Family name Kuz (Kuz , Куц , Куз ) , around the globe, is a common surname. The family name Kuz is characteristic of Eastern Europe, particularly Ukraine, where it is quite a common surname, Belarus, where it is quite a rare surname, and Russia. Not in comparison with a country's population, the name is most common in Ukraine, Russia, and Turkey. Very seldom, Kuz is the forename as well as the last name.