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Surname Heigh (Heigh ) , around the world, is a rare family name. The last name Heigh is characteristic of Canada, where it is a rare surname, New Zealand, and the United States, where it is a very rare surname. Not in comparison with a country's population, the name is most common in the United States, Canada, and the United Kingdom. Very seldom, Heigh is the forename as well as the last name.