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Last name Rinc (Ring , Rink , Rinc ) , in all the world, is a common surname. The last name Rinc is habitual in Ireland, where it is quite a common surname, Estonia, and Myanmar (explore the name in all countries). Measured by absolute frequency, the name is most common in the United States, Germany, and Myanmar. Much less frequently, Rinc is the forename as well as the last name.