The movie is going to be very similar to Return of the Jedi.

Rey and Kylo feel a tremor in the force and go to the old destroyed death star. They meet and fight, of course Rey wins. Rey feels guilty for leaving him to die. She questions herself and almost gives up on being a Jedi. But she decides to move forward and goes on to find Darth Sidious and finds out she is the grand daughter of Sidious.
Meanwhile Kylo heals up and has a coming to Yoda experience. He decides to be good and goes by Ben Solo. He knows Rey is going to Sidious and she will need his help. He goes and trys to save Rey, however Sidious is just too strong. Sidious throws Ben Solo down an endless pit and we never see Ben again. Rey who is about defeated gets help from the force ghosts of Yoda, Luke, Anakin and Obi-Wan. With Her new energy she faces Sidious and of course defeats him.

After the events she decides to take on the Skywalker name. And that is the reason for the movie title.