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Surname Minaj (Minaj , Минай , Минаж ) , in the world, is quite a common last name. The surname Minaj is characteristic of Albania, where it is quite a rare surname, Cameroon, and Botswana. Not in comparison with a country's population, this name is the most popular in India, Cameroon, and Ghana. Also, Minaj is the forename as well as the last name.