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Family name Конни (Connie , Conny , Konni ) , around the world, is a common surname. The last name Конни is habitual in Hong Kong, where it is quite a common surname, Nicaragua, where it is quite a rare surname, and Macao. Measured by absolute frequency, it is the most numerous in India, Malaysia, and China. Much more prevalently, Конни is the forename as well as the last name.