There are times when your behavior in public should deviate from your behavior in private, but never for the purpose of deceiving others. Instead, it is about withholding the parts of yourself that they cannot presently understand or which they are not yet worthy of knowing. Perhaps the easiest example of this is in the form of boundaries you might have that distinguish the parts of yourself you expose to others: coworkers versus friends, friends versus family, family versus your spouse, and your spouse versus God. Honesty precludes presenting a false self in any of these scopes, but each scope consists of withholding some different level of intimacy.
The principle of appropriately withholding intimacy ought to be applied at the individual level: Although you should never pretend to be someone other than who you really are, it is always going to be the case that you limit the extent to which you reveal yourself. This raises the vital question: how do you determine how much of yourself to reveal?