I tend to run it such that every character has two alignments.

Your "perceived" alignment is how you view yourself. This governs what classes you can take, how your own abilities affect you, and so forth. Gods might still disagree with you, depending on how egregious your behavior is.

Your "actual" alignment is how your actions square up in terms of D&D's objective morality. This governs how the spells and abilities of others affect you. A paladin can smite evil, even if the evil thinks that it is good.