Rey is the granddaughter of Emperor Palpatine. She is not biologically related to Anakin Skywalker.
But that itself ended up not being the final revelation, as Rey was firmly connected as Emperor Palpatine's granddaughter (yes, the Emperor Palpatine) in The Rise of Skywalker. The culmination of that movie saw her reject that family and instead carry on the mantle of the Skywalker name.
At the end of Star Wars: The Rise of Skywalker, Rey visited Luke's childhood home on Tatooine. 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.
From Star Wars: The Force Awakens' opening day, fans had their theories, and Star Wars: The Last Jedi seemed to squash all of them only for Star Wars: The Rise of Skywalker to provide a surprising answer: Rey is Emperor Palpatine's granddaughter, and her father a genetic strandcast (not quite a clone) of the Sith lord.
In addition to rejecting Sidious, Dathan married a woman named Miramir, whom he fell in love with. Together, they conceived a child, their daughter Rey, who was born in 15 ABY. Although he renounced the Sith Eternal and his donor, the Palpatine bloodline would prosper through him, just as Sidious predicted.
Powerfully Force-sensitive, Rey trains to be a Jedi under siblings Luke Skywalker and Leia Organa, and faces adversaries such as Kylo Ren, Supreme Leader Snoke and the resurrected Emperor Palpatine—who is revealed to be her grandfather in The Rise of Skywalker.
After years of speculation, Star Wars: The Last Jedi revealed that Rey (Daisy Ridley), the main character of the new trilogy, is not the child of Luke Skywalker (Mark Hamill). In fact, she's the child of “nobody” — per Rey's own words.
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.
And in The Rise of Skywalker we finally learn that Rey is actually the granddaughter of Palpatine. Her parents—one of which is the child of Palpatine—abandoned her on Jakku to keep her safe from her grandfather who was aware of her power.
But Rey responded that she was all of the Jedi. Aided by the spirits of the Jedi who had come before her, she used both Luke and Leia's lightsabers to deflect Sidious's Force energies back at him, destroying the Sith Lord once and for all.
She does not have a baby bump, her hand never goes to her stomach to indicate she's carrying a child, and there wasn't exactly any time for her to have conceived a child with anyone in the course of the film, including Kylo Ren/Ben Solo.
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.
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.
Master Yoda has risen above all others to claim the top spot as the most powerful Jedi of all time and the true chosen one according to IGN's audience. He won pretty handily as well, as he was victorious in 89,756 of his 95,243 battles and had a win percentage of 94.2%.
Rey is a member of the Skywalker family. Rey is not a part of the Skywalker bloodline. These two statements are not mutually exclusive. This is not a difficult concept to grasp.
Her lineage is "Palpatine". I'm sure you can understand why she chose to be called "Rey Skywalker" rather than "Rey Palpatine". Or "Rey nobody". After Luke, Leia and Ben's death, Rey, now the last Jedi, takes the name of Skywalker as her surname, continuing on the legacy of bravery, sacrifice, and strength.
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.
Abrams has given a very off-the-cuff interview in which he says Rey and Kylo Ren are like “brother and sister.” This, of course, makes it seem like their seemingly romantic kiss at the end of The Rise of Skywalker was incest.
By the end of The Rise of Skywalker, Rey had become the last known Jedi of the Skywalker Saga. With all that being said, Rey was not left as the last remaining Force-sensitive character.
Triclops Palpatine (son) Kendalina (daughter-in-law) Ken Palpatine (grandson)
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.
And then, wonder of wonders, she leaned forward and kissed him. A kiss of gratitude, acknowledgement of their connection, celebration that they'd found each other at last.
That's ok, but a little disappointing. Since The Last Jedi outright says Rey's parent were not important (from a certain point of view), and Luke shows no indication that he knows who Rey is, or even cares, it'd be really hard to justify that original idea.
The birth of Zayne
Zayne was born to his mother Rey Palpatine in the year after the Battle of Exegol, through mysterious and perplexing circumstances. His father could not have been Ben Solo, he died before Zayne could have been conceived whilst Rey was not intimate with a single man either.
She replies, "Myself," to which Luke says, "Because you're a Palpatine. Leia knew it, too" This realization takes Rey by surprise, as there had been few hints about her heritage up to that point.