I will say that it does seem slightly strange for Rey, whose arc is supposed to be about accepting people based on their heart, that her final moment in the movie is her taking on the name of Skywalker. Without any further clarification, one might assume she does this because she feels it gives her value, or purpose.
I know that in my novelization edit where Ben lives, I am planning on having Ben arrive on Tatooine. That’s when she becomes Rey Solo, not because that gives her a value or purpose, but because they are two individuals making a commitment to each other.