I'm going to go against the grain here and say it's generally fine. Of course if they want it written into the story in some meaningful way then the DM needs to know about it, but it could just be something they've never told anyone before, something only the character knows (their family, friends, other NPCs etc. don't know either). Once it's been revealed, they and the DM can work together if necessary to work out if there's potential there for it to affect a character arc or the wider story, but I don't think PCs having secrets that even the DM doesn't know is always a problem, and IMO can create some interesting spontaneous character moments if handled correctly.