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Surname Gunness (Gunness ) , around the world, is quite a rare last name. The family name Gunness is habitual in Mauritius, where it is quite a common surname, Trinidad and Tobago, and New Zealand, where it is a rare surname. In absolute terms, it most frequently occurs in Mauritius, Trinidad and Tobago, and the United States. Very seldom, Gunness is the forename as well as the last name.