Warning: SPOILERS for Star Wars: The Rise of Skywalker ahead.
scavenger life she had been living on Jakku.
The final scene of the film answers all of those questions while tying a ribbon around many central themes of Star Wars. Star Wars: The Rise of Skywalker's ending has Rey go the Skywalker home planet of Tatooine. The saga ends where it began as Rey ventures into the home that Luke Skywalker was raised in. Here, she buries the two Skywalker lightsabers. One belonging to Anakin and Luke Skywalker, the other to Leia Organa. As she rises, an older woman mentions how no one has been to the Lars homestead for years and asks Rey her name. Here Rey pauses, not exactly knowing how she should answer the question that has been her life's goal to find. The Rise of Skywalker had revealed that Rey is a Palpatine. Carrying the Palpatine name is even more tragic than her feeling that she is a nobody, as said in The Last Jedi.
Throughout The Rise of Skywalker, the revelation that she is a Palpatine, that her destiny is to become Empress Palpatine, a Sith Lord, brought her closer to the dark side than ever before. She displayed more anger, hate, and Sith techniques like Force Lightning throughout the film. It was not until the Force ghosts of Luke and Leia looking back at her in true George Lucas fashion. The two smile at her, giving her the confidence to look back at the woman and call herself Rey Skywalker. The significance of Rey using the name of Luke and Leia should not be understated.
The Skywalker saga of Star Wars has always revolved around the concepts of bloodline and fate. Much like Anakin Skywalker was tied down to his fate as the Chosen One, Luke and Leia bore the responsibility to atoning for Anakin's sins and ultimately redeemed him, bringing balance to the Force. Kylo Ren, by contrast, was also bogged down by his own bloodline, looking towards Vader as his ultimate goal, instead of Luke, Leia and Han Solo. Kylo's fear was never living up to his own grandfather, giving many opportunities for Palpatine, who used Snoke, to manipulate him. Rey, on the other hand, never truly knew who she was until the end of her journey.
Both Luke and Leia were aware that Rey was a Palpatine, yet each still took time to train her to be the final hope of the Jedi. In many ways, both Leia and Luke served as Rey's parents, raising her into the Jedi she was meant to be. In the final moment of Star Wars: The Rise of Skywalker, Rey is left with the choice of calling herself Rey Palpatine as her bloodline would suggest, or Rey Skywalker, carving her own destiny and fate. As the sequel trilogy spent time in the building, Rey's final decision was obvious. She would abandon the Palpatine name, which ends that family's legacy and instead takes on the name of a family that has earned her respect, Skywalker.