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Family name Enni (安妮 , Enni , Энни ) , throughout the world, is a common cognomen. The family name Enni is characteristic of Estonia, where it is quite a rare surname, Honduras, where it is a rare surname, and India. Measured by absolute frequency, this name is the most popular in India, China, and Indonesia. More prevalently, Enni is the forename as well as the last name.