I have a hidden Pyke and one other unit, opponent uses Falling Star on the other unit, I react with the Pyke, can they choose Pyke after it has revealed or does their choice stick?

No — their choice sticks. Falling Star's targets are locked in when it's placed on the chain; revealing Pyke doesn't give them a new choice.

When your opponent plays Falling Star, they choose both "Deal 3 to a unit" targets at finalization (Rule 355.5/355.6). Per Rule 355.15, those choices can't be changed afterward unless a spell or ability says otherwise — and your hidden Pyke wasn't even a legal target at that point, since a facedown hidden card isn't a unit on the board. When Falling Star resolves, it deals its 3 (or 6, if both instances chose the same unit) to the original target, and your freshly revealed Pyke is untouched.

The reveal itself is legal (a hidden card gains [Reaction] while facedown, Rule 811.6), it just doesn't affect who Falling Star is pointing at.