This, of course, is the obvious answer. In The Force Awakens, Rey went through a hero’s journey, similar to Luke in A New Hope. She started her connection to The Force in the previous movie, and (rather quickly) developed abilities and skills to use it Everything from mind controlling a Stormtrooper played by Daniel Craig to being able to engage Kylo Ren in a lightsaber duel, and even win against the member of the Knights of Ren who killed all the new Jedi that Luke was training.
However, because she is the obvious choice, it seems that it must be a red herring. First off, she’s not a Jedi Knight right now and has not earned the title. She may do so in the upcoming film, so we’ll have to wait and see.
Another reason is that she may not become a Jedi and turn to the dark side. In both the screenplay and the novelization of The Force Awakens, Rey hears a voice that is either Palpatine or Snoke’s when she is experiencing her vision at Maz Kanata’s castle and when she is fighting Kylo Ren. If Luke doesn’t properly train her, she may end up coming under Snoke’s tutelage and become one with the Dark Side of the Force. Therefore, she will not be a Jedi and not the last of them.