In the original universe, the name of the mall was Twin Pines Mall. As a side effect of Marty traveling back in time, one of the pines was killed. This affected the space-time continuum, and created a ripple in time which changed future events.
From Marty's point of view, he is travelling outside of that version of the timeline, so in his mind, the name of the mall should be Twin Pines Mall. The Marty he runs into at the end of BTTF is actually in an alternate reality. To Marty 2, the mall has always been called the Lone Pine Mall, and he possesses no memories of the alternate version of reality. This aspect of time travel is known as a causal loop. Marty's past actions are affecting alternate versions of himself.
In the next iteration of the loop, Marty 2 would actually still drive over one of the pines with the DeLorean, and leave one still standing. Because the original Marty ran over the tree, all future versions of him will also do the same thing. This is called a predestination paradox. Basically, Marty's actions when he first traveled back in time will repeat forever unless an outside action is taken upon on it such as time travel which directly affects Marty.