The ending of Star Wars: The Rise of Skywalker has Rey defeat Emperor Palpatine, Ben Solo die, and Rey take the name Rey Skywalker on Tatooine.
What actually happens on Exegol? Rey turns Palpatine's Force lightning back on him, using the lightsabers of Luke and Leia. Both Skywalker weapons are in her hands at the decisive moment, and in my opinion that is the film's clearest statement of theme: she wins with the inheritance of two people, not alone. The detail also gives Leia a physical presence in the climax, and it is worth remembering that Carrie Fisher appears in the film through unused footage from The Force Awakens.
What does Ben Solo's death mean? Ben gives the last of his Force power to bring Rey back to life, and he dies. In my opinion this is the film's answer to the Kylo Ren and Rey story across the sequel trilogy, since the credit itself, Kylo Ren / Ben Solo, tracks the two sides of the character. Ben's sacrifice is his own choice, made after Palpatine offered him a fleet for killing Rey.
Why does Rey say Rey Skywalker? Rey calls herself Rey Skywalker because the name is her own decision, made after she buries the lightsabers of Luke and Leia on Tatooine. In my opinion, the scene is about the name as a choice, because the buried sabers close the weapons' story while the name carries the family forward.
Is Rey the daughter of Luke Skywalker? No. Rey takes the Skywalker name at the end by introducing herself as Rey Skywalker, and the film closes the Skywalker saga and the sequel trilogy.
How does this ending compare with the rest of the series? In my opinion, the film is built as a reply to the two films before it. Star Wars: The Force Awakens is the other end of the sequel trilogy, and the finale links back to it directly because Carrie Fisher's Leia is assembled from that film's unused footage. Star Wars: The Last Jedi is where the previous story stopped, on Crait, and this film begins a year after those events, so its opening has to carry that film's aftermath before Palpatine's broadcast changes the stakes. Return of the Jedi sits at number 3 in release order, while this film is number 12 and is the third part of its own trilogy, so both are final chapters of a run of films. I make that comparison on structure only, not on quality. If you want to keep reading, our Star Wars timeline page places the film in the larger story.