What you keep private can still be completely honest.

Honesty is about not misrepresenting, not about full disclosure. You can decline to discuss your salary, your health, or your marriage and still be a completely truthful person. The two get conflated so often that people feel dishonest simply for having an interior life. Nothing is being falsified by a boundary.

If you feel dishonest for keeping something private, ask whether anyone is being misled by the absence. Usually they are not. Saying nothing and saying something false are different acts entirely.