Well, a new Star Wars tie-in has finally answered that question. In The Rise of Skywalker's novelization, we learn that Rey's father was a failed clone of Emperor Palpatine. He was initially created to be a vessel to house Palpatine and his Sith power.
Father of Rey
Dathan had a relationship with Miramir, who gave birth to their daughter, Rey. 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.
Rey. Rey (portrayed by Daisy Ridley) is the granddaughter of Sheev Palpatine/Darth Sidious through Dathan. Born on the planet Hyperkarn in 15 ABY, as a child in 21 ABY, Rey was abandoned by her parents on the planet Jakku to protect her from Sidious.
Eventually, another three-eyed child, Triclops, was born. Rumor had it that his mother was Palpatine's Umbaran aide Sly Moore, who had impregnated herself using DNA from an undisclosed source.
It is subsequently revealed that Palpatine had a son (who was his clone) whom he named Dathan, who renounced him; he and his wife, Miramir took their daughter Rey to the planet Jakku, assuming lives as "nobodies" to keep her safe.
Despite being enemies, Rey and Kylo Ren share a connection called a 'Force dyad' and eventually become romantically involved with one another. Following Palpatine's final defeat and her own resurrection, Rey adopts the name Rey Skywalker to honor her mentors and their family legacy and renounce her lineage.
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.
Although Star Wars: The Rise of Skywalker concludes with Rey choosing the name of Skywalker and completing her path to becoming a Jedi, it's possible that she was actually the reincarnation of Anakin all along.
In The Phantom Menace, when Qui-Gon Jinn meets tiny Anakin Skywalker and his mother, he goes on about how the Force is like, crazy strong with Anakin or whatever, and then asks his mother about Anakin's dad. Shmi Skywalker is pretty clear in her answer: There isn't a father. She was impregnated by the Force.
We know for a fact that Sheev Palpatine, Darth Sidious himself, had one son. Whether biological or the result of cloning, this son seemed to be a complete unknown to viewers and the galaxy until The Rise of Skywalker.
Rey, despite learning she's the granddaughter of Sheev Palpatine, chooses to call herself a Skywalker. It's her choice. She could have called herself anything. But rather than handcuff herself to her Palpatine bloodline, she decided to take the name of the heroes who came before her.
In the canon comic Darth Vader No. 25, it is revealed that Palpatine somehow used the Force to manipulate midichlorions to impregnate Shmi 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.
In Star Wars: The Last Jedi, we got an answer to the question of Rey's parents: they were nobodies.
In The Rise of Skywalker's novelization, written by Rae Carson, it's revealed that Rey's father is a failed Palpatine clone. He was initially created as a vessel to house the Sith Lord but proved incapable of doing so.
At first, most fans assumed Rey was the daughter of either Luke Skywalker or Obi-Wan Kenobi. And during a 2020 interview on Jimmy Kimmel Live, Ridley was asked if she knew about Rey's parentage from the beginning. She replied, "No.
Attended by medical droids, Padmé Amidala gave birth to her twins Luke and Leia on Polis Massa. She died and the twins were split up, with Obi-Wan taking Luke to Tatooine and Bail Organa returning home to Alderaan with Leia.
Owen Lars was a human male from the desert planet Tatooine who worked as a moisture farmer. He was the son of Aika and Cliegg Lars, and he became the stepbrother of Jedi Knight Anakin Skywalker when Cliegg married Anakin's mother, Shmi Skywalker.
Rey is Anakin's half sister, and Palpatines relations to Rey through the force. Rey is a genetic experiment/force experiment of immaculate conception orchestrated by palpatine. So Rey is Palpatines daughter or grand daughter, in a metaphorical sense. The same way Anakin is Palpatines son through the force.
So, as far as the canon goes, yes, Rey is considered a Skywalker. It's just like how any adopted child would be considered a member of the family that they were brought into. Depending on which Star Wars fan you ask, the identity of Rey will vary. Some would consider her a Palpatine because of her blood.
In The Rise of Skywalker, more develops about that story. After his confrontation with the phantom Emperor Palpatine, the new Supreme Leader learns that she is in fact the granddaughter of the Dark Lord of the Sith himself. And in a way is also his daughter. Rey's father was a genetic clone of the Emperor himself.
Luke's Force ghost then emerges to teach her about facing her fears, asking about what she's most afraid of. 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.
Affiliation(s) Zayne Skywalker was a force-sensitive Jedi Knight, and the son of Ben Solo and Rey Palpatine, a dyad in the force as the grandson of the Chosen One and the son of power force wielders, who became a legendary warrior and hero for the galaxy in the decades after the Battle of Exegol.
Miramir was a human female who worked as a junk trader during the New Republic Era. Her husband Dathan was the cloned "son"—an artificial Strand-Cast—of Darth Sidious, the Dark Lord of the Sith and Galactic Emperor. Miramir had a Force-sensitive child with Dathan, a daughter named Rey, who was born in 15 ABY.
And through it all, we learned very little about Rey's parents. For instance, what were their names? That question is answered in the new Star Wars novel Shadow of the Sith by Adam Christopher. In a new excerpt, it's revealed that the names of Rey's parents are Dathan and Miramir.