One character in the story lies and tries to keep secrets, because his reputation would be ruined if the truth got out. For me, if you’re lying about something just to keep a certain reputation then the reputation you want probably isn't good anyway. If you can’t keep your reputation without lying then you don’t need it at all.
One thing I’ve lied about to keep a reputation is caring. I’ve always told people that I don’t care about a lot of things, and the result was them believing I don’t care about anything. Because of this, it made them stop asking me questions about