In Star Wars Episode IX: The Rise of Skywalker we learn that Rey's grandfather was
Who was the grandmother?
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Material released since TROS has confirmed that Rey's father, Dathan, was a "Strand-Cast", a type of clone. According to Palpatine himself:
Using a technique known as Strand-Casting, countless modified clone bodies were produced from my genetic template. All but one of them were utter failures.
This is supported by a scene in the TROS novelization where Rey is able to pick up Palpatine's thoughts:
The heretics of the Sith Eternal toiled, splicing genes, bolstering tissue, creating unnatural abominations in the hope that one of these strandcasts would succeed and become a worthy receptacle. The heretics would do anything, risk anything, to create a cradle for their god-consciousness.
Nothing worked. But their efforts were not entirely in vain.
One genetic strandcast lived. Thrived, even. A not-quite-identical clone. His "son." But he was a useless, powerless failure. Palpatine could not even bear to look upon such disappointing ordinariness.
The boy's only worth would lay in continuing the bloodline through more natural methods.
And it was through that eventual union, unexpected as it was, that Rey was born. The perfect vessel. Strong enough to contain all the power of the Sith. His granddaughter...
Source: The Rise of Skywalker: Expanded Edition; Kindle edition, page 284
There was no grandmother.
While it is not revealed in the movie, the official novelization is rumored to claim that as part of his contingency, Palpatine prepared a clone before being thrown down the Death Star II shaft by Vader as he sensed the flicker of light within the latter. Before his body hit the ground, he had learned to project his essence into one of the Clones. This was an imperfect clone. Palpatine's son (Rey's father) is also a clone. The son is one of the clone projects of Palpatine because they kept trying to make a body for him to contain his power. The son is a perfect bodied clone. Palpatine hated the son for being a failure as he had no Force abilities. Note: the novel itself has not been released yet and many revelations that are being reported are only available as "leaks".