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Family name Damour (Damour , Дамур , دامور ) , all over the world, is quite a common last name. The cognomen Damour is habitual in Reunion, where it is quite a common surname, France, where it is quite a rare surname, and Rwanda. Measured by absolute frequency, the name is most common in France, the United States, and Reunion. Much less frequently, Damour is the forename as well as the last name.