Spanish Meaning: The name Salvatore is a Spanish baby name. In Spanish the meaning of the name Salvatore is: Savior. American Meaning: The name Salvatore is an American baby name.In American the meaning of the name Salvatore is: Savior. Italian Meaning: The name Salvatore is an Italian baby name.In Italian the meaning of the name Salvatore is: Savior.n American the meaning of the name Salvatore is: Savior. Italian Meaning: The name Salvatore is an Italian baby name. In Italian the meaning of the name Salvatore is: Savior.