I know it’s not super popular, but it is canon, so how about something to do with Palpatine creating life? If he was involved in Rey’s origins in a similar way to how he was for Anakin, that would both make her his inheritor (‘granddaughter’ due to the age difference) and make her claim to be a Skywalker more logically valid. It would also explain why her parents want to get her away from him (they don’t want that life for their daughter), and why Ochi hunted her, and explains why he either wants to kill her (a threat) or capture her (an inheritor or even vessel). It’s also an option that will most likely be futureproof in the case of future content referring to her being his ‘granddaughter’, having his blood in her veins, or similar. Arguably, it keeps her as a nobody too, in a similar way to young Anakin born to Shmi.

It’d also now add a nice bit of irony in that, while it is a bit of a rehash, he’s now two for two in force-children turning against him and towards the light.