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Family name Addai (Addai , Аддай , أدي ) , in all the world, is a common surname. The family name Addai is characteristic of Ghana, where it is quite a common surname, Curacao, and Qatar, where it is a rare surname. Not in comparison with a country's population, this name is the most popular in Ghana, the United States, and the United Kingdom. Much less frequently, Addai is the forename as well as the last name.