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Last name Kozak (Kozak , Kosak , Козак ) , around the world, is a common surname. The surname Kozak is habitual in Eastern Europe, particularly Ukraine, where it is quite a common surname, Slovakia, and Hungary (explore the name in all countries). Not in comparison with a country's population, this name is the most popular in Ukraine, Poland, and the United States. Likewise, Kozak is the forename as well as the last name.