She was taught by Luke for a third of the movie. That's how she learned to utilize her powers for good. She is the last Jedi because Yoda burned the sacred Jedi texts.
We don't need to use spoilers, I think people get what this thread is about at this point
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He didn't burn them, Rey stole them (this is shown in the movie's final scene, i missed it the first time I watched it) and Yoda only set the tree on fire. When Yoda says "Rey already has all the information in those books." He isn't making some corny metaphor, he is speaking very literally. She literally has the books lol.
here’s an example: the title
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Leia, Rey, and Kylo are also force sensitive (one could argue Poe and Finn might be as well). "Jedi" simply refers to the religious order in which users of the "light" side of the force follow. Luke would be The Last Jedi because technically Rey is not a Jedi yet and it is totally up to her whether or not to rebuild the Jedi Order.