In “Back to the Future,” the time machine is first tested at Twin Pines Mall. Doctor Emmett Brown chooses the shopping-center parking lot for his initial full demonstration of the converted DeLorean.
The test sends the DeLorean one minute into the future under remote control, with Doc’s dog Einstein inside. Einstein becomes the first time traveler in the film’s story. The experiment demonstrates the car’s time circuits and flux capacitor before the more dangerous events involving Marty McFly and the Libyan terrorists.
The location’s name later changes because of Marty’s accidental trip to 1955. While fleeing through the past, he runs over one of the two pine trees on the property of farmer Peabody. When Marty returns to 1985, the shopping center is now called Lone Pine Mall, reflecting the altered timeline.
The key distinction is between Twin Pines Mall and Lone Pine Mall: both names refer to the same fictional shopping center at different points in the film’s timeline. Hill Valley Mall is not the canonical name, even though Hill Valley is the fictional town where the story takes place.