Star Wars: The Rise of Skywalker revealed that Rey had been a descendant of Palpatine all along. And while that comes as a shock to most, Luke's Force ghost claims to already know about the dark secret. However, with the Jedi Master giving no indication of that during The Last Jedi, Star Wars fans have been left wondering when exactly Luke found out who Rey truly was.
After her fight with Kylo Ren on the ruins of the second Death Star, Rey travels back to Ahch-To, wanting to go into hiding. Luke's Force ghost then emerges to teach her about facing her fears, asking about what she's most afraid of. She replies, "Myself," to which Luke says, "Because you're a Palpatine. Leia knew it, too" This realization takes Rey by surprise, as there had been few hints about her heritage up to that point.
Now, Luke may have known that fact even before meeting Rey, as before he went into hiding, Luke and Lando traveled across the Galaxy to investigate any possible Sith tracks. While they eventually parted ways, Lando's trail had led him to Pasaana, where he found the remanence of the Sith servant -- Ochi. Palpatine sent the assassin to hunt and kill his clones and granddaughter, so there's a chance Luke knew of Rey's existence through that discovery.
However, their first meeting in The Last Jedi makes it seem like Luke genuinely doesn't know who Rey is. But it's possible that Luke came to realize who Rey was as he began teaching her, as his connection to Rey grew during his lessons. The main reason that scenario is possible is that Luke was closed off from the Force when he initially met Rey, meaning he couldn't have sensed who she was until came back to him. But even more important than that, Luke felt the darkness in Rey as she began connecting to her surroundings.
As he taught Rey to meditate, she sensed the cave under the island and headed right to it. Luke woke her up, saying, "You went straight to the dark," before explaining that he's "seen this raw strength only once before, in Ben Solo. It didn't scare me enough then. It does now." While that statement can be attributed to Rey's connection to the Dyad in the Force, it could also have been the moment Luke began suspecting who Rey really was, especially if he knew about the Palpatine clones
If Luke did find out about Rey's heritage during her training, it would've taken a lot of restraint to hold back, which is why some assume that Luke found out after becoming a Force ghost. While the details of Force ghosts are a mystery, they likely gain a massive amount of knowledge after becoming one with the Force. And so it could be that Luke found out through the Force and didn't mention it until the time was right.
What confuses things further, however, is the fact Leia knew as well. If Luke found out about Rey before going into hiding, it means he would've told Leia about her existence, and she would have to have figured it out on her own. But if Leia found out later, it means Luke appeared to her as a Force-ghost to reveal the information. Either way, a clear point for finding out about Rey Palpatine hasn't been given, but it seems to have been around the time of The Last Jedi. Luke's discovery of Rey's power and his re-connection to the Force would explain his behavior towards her throughout the movie and give Luke time to explain the situation to Leia as a Force ghost.