Star Wars: The Rise of Skywalker revealed that Rey is a Palpatine, and then had her claim the Skywalker name at the end - but Anakin's origin means the latter would work better if she was a nobody. Rey's parentage was the question of the Star Wars sequel trilogy.

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.