Opp gjennom årene har turneringen endret navn en rekke ganger. Den har hett Tucson Open, Tucson Open Invitational, Home of the Sun Open, Dean Martin Tucson Open, NBC Tucson Open, Joe Garagiola-Tucson Open, Seiko-Tucson Match Play Championship, Seiko Tucson Open, Northern Telecom Tucson Open, Northern Telecom Open, Nortel Open, Tucson Chrysler Classic, Touchstone Energy Tucson Open og i dag altså Chrysler Classic of Tucson.