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Last name Ourai (Ourai ) , in all the world, is a very rare surname. The last name Ourai is habitual in Morocco, where it is a rare surname, Thailand, where it is a very rare surname, and France, where it is an extremely rare surname. Measured by absolute frequency, this name is the most popular in Morocco, Thailand, and the United States. Much less frequently, Ourai is the forename as well as the last name.