The name Ines is an American baby name. In American the meaning of the name Ines is: Chaste. Greek Meaning: The name Ines is a Greek baby name. In Greek the meaning of the name Ines is: Kind or innocent.Spanish Meaning: The name Ines is a Spanish baby name. In Spanish the meaning of the name Ines is: Meek.Chaste.he name Ines is an American baby name. In American the meaning of the name Ines is: Chaste. Greek Meaning: The name Ines is a Greek baby name. In Greek the meaning of the name Ines is: Kind or innocent.