At the start of the film, when Doc is shot and Marty escapes the Libyans by traveling to 1955, it takes place in the parking lot of THIS MALL. When Marty returns early to try and save Doc (and in turn witnesses his own escape), it has a different name thanks to Marty's actions in 1955 (which were about to happen again).
Twin Pines Mall [the mall was Lone Pine Mall upon his return due to his running over one of the pine trees on the farm in 1955]