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Last name Boccia (Bocha , Bocsa , Boccia ) , in all the world, is a common surname. The last name Boccia is characteristic of Italy, where it is quite a common surname, Romania, where it is quite a rare surname, and Paraguay. Not in comparison with a country's population, this name is the most popular in Italy, India, and the United States. Much less frequently, Boccia is the forename as well as the last name.