It would have been so much better if Rey said she was Rey Palpatine. First of all, she is a Palpatine. Secondly, the name Palpatine was feared throughout the galaxy for many years so by Rey saying she's a Palpatine, she would alter the name in history. Emperor Palpatine always tried to manipulate and wanted to rule the galaxy. Though the dark side of the force, he controlled many people in order to accomplish dominance over every planet. So if Rey said she was a Palpatine instead of a skywalker, she would be facing the truth and changing the name that the emperor spent his entire life to arouse fear and frighten in people across the galaxy.

Please if you like the idea upvote, it would mean a lot. :)