Then there's this explanation. By the end of the movie, the Skywalker bloodline is completely extinct, with the last survivors — Leia and Ben — becoming one with the Force. Leia certainly rose to the occasion of being the last Skywalker in this movie, complete with being addressed as a Jedi master and finally getting to wield a lightsaber in a flashback. Despite the ending of the genetic line, the name Skywalker rises again almost immediately, with Rey's choice to use the name as her own. This is more in line with previous theories that "Skywalker" would somehow become an honorific or a title rather than just a name.
It's not outside the realm of possibility that Rey is on her way to start a brand-new order of Force users. Now that "a thousand generations" of Jedi live on through Rey, the old ways of the Jedi might not be the focus, but a new way of dealing with the Force. And Rey isn't the only one with a Force connection: Finn is revealed to be Force-sensitive too, and we can assume there are plenty more. Perhaps Rey's taking on of the Skywalker name is a nod to the fact that anyone can take on the mantle of those who are connected to the Force, in ways both great and small.
