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Surname Cucui (Cucui , Цуцуй ) , all over the world, is a rare last name. The surname Cucui is habitual in Romania, where it is quite a rare surname, Argentina, where it is a very rare surname, and Ukraine, where it is an extremely rare surname. Measured by absolute frequency, the name is most common in Romania, Argentina, and Russia. Very seldom, Cucui is the forename as well as the last name.