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Last name Terenzio (Terenzio , Terentius ) , around the globe, is quite a rare cognomen. The family name Terenzio is habitual in Italy, where it is quite a rare surname, Argentina, where it is a rare surname, and Canada, where it is a very rare surname. Measured by absolute frequency, it is commonest in Italy, the United States, and Argentina. More frequently, Terenzio is the forename as well as the last name.