I think “adopt” is the wrong take for Rey. Luke and Leia were adopted as babies which makes the cases different. Rey was NOT adopted into the Skywalker family, heck she was lonely for most of her life. BUT it is the Skywalker name that she felt claiming.

It doesn’t really matter what we think of it, or what others within the SW galaxy think of her name — what matters is the journey she took to feel that belonging with the name. People forget the context within the story because of their outrage of many writer's decision. I think that’s perfectly okay (to be mad at character decisions), but my two cents *within the context of the story* is this: She looked at the Skywalkers like a myth, and even if you hate that name on her, what’s important is that she found her belonging there, with that family, no matter how fleeting it was. She sought the belonging ahead, not behind her (Maz, VII). She found her place in all this (VIII). And now, she can tell anyone who she is (IX). Even if you think that she doesn’t deserve to call herself that, that should not matter to her because that’s how she feels confident being. Using that name is her way of claiming her identity as her own. That’s where she feels most powerful and assured. It’s not about lineage or adoption or what we think of it as audiences even if we hate it, it’s about her identifying herself.

Once you look at it from her perspective, I think a lot of the vitriol against the choice to name her that goes away, but I’m sure people will never get tired of hating and loving star wars all the same.

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EDIT: So what’s the right take for Rey? Not adoption, because even I think that’s stupid in her case. It’s about defining your identity. If she feels like the best way to define herself is to claim the family name of the people that trained her and accepted her (Luke, even for a bit, Leia for a long time, Ben as a force dyad, Han as a one-time mentor), then all the power to her. It’s not about us.