It could be kinda interesting for Rey to visit Tatooine on a personal level. It’s her realizing that she had similar humble beginnings on a desolate planet as Luke did. Both planets of Tatooine and Jakku are intertwined with pain and suffering, but it doesn’t change how their environment had a huge impact in shaping their identity. She took on the Skywalker name on a superficial level since she didn’t have a lastname for most of her life. On a deeper level, embracing how she and Luke had similar paths, it’s her believing that she’s been a Skywalker this whole time, not in blood, but in character. Rejecting Palpatine is the smart choice since we have no idea, for one, how he came about and most likely different from how Rey grew up. I’ve read where many fans think she should had embraced Palpatine as a last name. I say no because just imagine Luke throwing away Skywalker in favor of Vader. Luke Vader. Doesn’t work, does it? Vader and Palpatine carries too much negativity and baggage. It’s like the real life equivalent of taking on the lastname Hitler, rationalizing it by saying you will do good deeds and flip people’s view towards that name. Good luck with that.
No, Skywalker has more positive symbolism and more influence on Rey than her bloodline.

None of this analysis is meant to prop this ST up as some masterful writing, but just to illustrate that with the proper writing, this would had been communicated to the audience much smoothly.