If it acts like a duck (all the time), it's a duck. Doesn't matter if the duck thinks it's a dog, it's still a duck as far as the rest of us are concerned.
Authenticity, for me, is doing what you promise, not "being who you are".
That's because 'being' is too amorphous and we are notoriously bad at judging that. Internal vision is always blurry. Doing, on the other hand, is an act that can be seen by all.
As the Internet and a connected culture places a higher premium on authenticity (because if you're inconsistent, you're going to get caught) it's easy to confuse authentic behavior with an existential crisis. Are you really good enough, kind enough, generous enough and brave enough to be authentically a hero or leader?
Mother Theresa was filled with self doubt. But she was an authentic saint, because she always acted like one.
You could spend your time wondering if what you say you are is really you. Or you could just act like that all the time. That's good enough, thanks. Save the angst for later.