The son of
Even though Kylo Ren uses a red lightsaber, harnesses the dark side of the Force, and wears a cape, he is not a Sith. Because of that, he can never hold the title of Darth. Instead, he was just a chaotic mess of the dark side (until he eventually found his way back to the light).
But if Palpatine essentially fathered Anakin through the Force, the Emperor would be the great-grandfather of Kylo Ren and the grandfather of Rey, making the pair first cousins once removed.
What is the connection between Kylo Ren and Rey? As Kylo Ren himself says in The Rise of Skywalker, he and Rey are bonded not just by their familial legacies (Ren as the grandson of Darth Vader and Rey as the granddaughter of Emperor Palpatine) but by their unique connection in the Force.
The crux of the series is that Obi-Wan must rescue Leia from the clutches of the Empire. During this series, her bond with Obi-Wan, or “Ben,” results in something surprising: It legitimizes the naming of Leia's future son, Ben “Kylo Ren” Solo.
So, even when she eventually learns his real name, Leia always associated the Jedi Master with Ben rather than Obi-Wan. Inspired by this, it makes sense that she decided to name her son Ben Solo — after Ben Kenobi.
The simplest explanation is that Obi-Wan is using Ben as an alias, so that he can hide his identity from the Inquisitors and the rest of the Empire. Even if there are deeper reasons for the name, which we'll get into in a minute, this is most likely a large part of the reason.
“So Leia Force projects herself as Ben and uses her life force to save Rey. Even going as far as to kiss Rey to convince her it's Ben. It's why when Ben disappeared, so did Leia.”
Rey was born on Hyperkarn in 15 ABY during the rise of the New Republic. Her father, Dathan, was a bioengineered Strand-Cast cloned from the genetic template of Darth Sidious, the Sith Lord who ruled the Galactic Empire as Emperor Palpatine.
In the Jedi Prince series of young-reader novels (1992–1993) by Paul and Hollace Davids, set about a year after Return of the Jedi, a three-eyed mutant named Triclops is revealed to be Palpatine's illegitimate son; he had a son named Ken, the titular "Jedi Prince".
A crystal embodies the Jedi as the heart of the lightsaber, and pure kyber has no color until it's bonded to the Force user. This process likely resulted in Rey Skywalker's lightsaber being yellow.
While on the planet, when someone asked her who she was, Rey responded by saying that she was "Rey Skywalker." Although she wasn't related to them, both Luke and Leia had been mentors to Rey throughout the sequel trilogy.
The son of Han Solo and Leia Organa, Ben Solo was seduced by the dark side of the Force and renamed himself Kylo Ren: leader of the Knights of Ren, champion of the First Order, and apprentice to Supreme Leader Snoke.
You may have noticed that Snoke does not have the “Darth” title like the Dark Lords of the Sith do. He was never given one because he isn't technically a Sith Lord.
But a new tie-in novel, Shadow of the Sith by Adam Christopher, finally fixes this. Rey's parents are none other than Dathan and Miramir. No, that's not a typo. Her dad's name is Dathan, which is at least slightly better than Sheev Palpatine.
The Rise of Skywalker and the Resurrection of Palpatine
With his clone form far from full power and dependent on a support system that kept him (literally) attached to Exegol, though, Palpatine needed someone to work in his stead. For that he had his loyal followers build him Snoke (and many Snoke copies).
Anakin Skywalker is the son of Shmi Skywalker, born without a father through the Force. He is the secret husband of Padmé Amidala, the father of Luke Skywalker and Leia Organa, the father-in-law of Han Solo, and the maternal grandfather of Ben Solo.
Rey's lightsaber was a yellow-bladed lightsaber that was constructed by the Jedi Rey Skywalker following the First Order-Resistance War.
Reclaiming his identity as Ben Solo, the redeemed Jedi joined Rey on Exegol to save her from Sidious and defeat him once and for all, though the effort took Rey's life. When Solo sacrificed himself to revive Rey, he died and became one with the Force, joining his parents, uncle, and grandfather.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
So anyway, if you ever wondered why Obi-Wan Kenobi hated flying, here you go. It's all because of one moment years before TPM, where the autopilot of his ship took over and forced him to helplessly fly at high speeds through the narrow inner-workings of a massive ship.
Obi-Wan Only Says He Never Owned R2
Note that he says nothing about not recognizing R2; his clever dodge gives the impression that they're strangers but doesn't actually deny knowing the little astromech. Thus, there really isn't a "contradiction" in the first place—Obi-Wan was just being his cunning self.
Thanks to that scene, there are now two possible explanations for the sudden jump in Obi-Wan's physical age: it was a result of the Dark Side of the Force being used against him, or it was a result of the burns he suffered.