French Meaning: The name Adrianna is a French baby name. In French the meaning of the name Adrianna is: From Adria, the Adriatic sea region.Also means dark. American Meaning: The name Adrianna is an American baby name.In American the meaning of the name Adrianna is: From Adria, the Adriatic sea region.rench Meaning: The name Adrianna is a French baby name. In French the meaning of the name Adrianna is: From Adria, the Adriatic sea region.