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Last name Kainak (Kainak , Кайнак ) , throughout the world, is a rare family name. The family name Kainak is characteristic of Moldova, where it is quite a rare surname, Ukraine, where it is a very rare surname, and Georgia. Measured by absolute frequency, it is the most numerous in Eastern Europe, particularly Moldova, Russia, and Ukraine. Much less frequently, Kainak is the forename as well as the last name.