I find it kind of odd people think Kylo told Rey the truth.
Minimizing her lineage would be wise if she's a Skywalker.
Skywalker women get **** done. Padme, Leia, hopefully Rey.
Skywalker men are whiney babies. Anakin, Luke, Ben.
Kylo would be no match for a fully-realized Skywalker woman.
Also on if they intend to kill the Jedi, not have Rey be a Skywalker ...
Skywalker could be the new "way" of the Force.
Skywalker being the new way to yield the Force, that balances both Light and Dark.
Jedi = Light Side, Sith = Dark Side, Skywalker = Balance and/or the new Light Side religion.
Tons of possibilities here ...