The issue with her taking the name Skywalker is that it is a quixotic conclusion to her character arc. Rey spends three movies searching for a family, and ends by taking the name of a family that is now vanished from the galaxy. Sure, she feels comfortable carrying on the Skywalker legacy (at least the good one(s) anyway), but this does little to satisfy her need for a real living family in whatever form that takes. It’s a big missed opportunity because now there is a galaxy of young people who have been stripped of their parents, potentially forever. Will they all take the name Skywalker? Will Finn? There is no indication of this, and it throws into tension her emotional reunion with Finn and Poe, her presumed new ‘family’. The movie also seems to forget that Rey’s real parents died heroically to save her, so not taking their name is another instance of the film throwing a rake in front of itself to trip over.
Beyond these particular tensions, there is an even larger tension with the final scene, and it has to do with the hero’s journey. In the archetypal tale our hero goes forth on adventure and returns home fundamentally changed in some way. The final scene of a mythic tale gives answer to the final question regarding the hero, that of whether they will return to society or whether the journey has changed them too much to ever truly return. Frodo cannot return to the Shire, instead sailing to the Undying Lands to be healed. Luke does return to society in the final scene of Return of the Jedi, leaving the ghosts of the past to join in the celebration. So what does Rey do?
The penultimate scene of TROS implies that despite being changed by her journey, she will return to society and live happily among them. This is a sufficient answer and completes her arc. However the final scene flips this assumption. Now she is reviving the ghosts of the past through her name and ending the film alone on a desert planet. If she were merely going there to bury the past it wouldn’t necessarily be an issue, but the name implies a connection with this isolation that she will never be rid of. She both does and does not return to society simultaneously, and this is why I find it so frustrating.