I have a mix of alpha, beta, and "sigma" traits that fluctuate wildly depending on all the context.
Your personality is not a static thing, ever wonder why you act one way with your parents and a completely different way with your friends? That's not because you're a fake it's because you're literally not the same person when you're with different people. If someone insists on acting the same way around everyone it means they're too scared to be who they really are, which is actually nothing at all, and that terrifies people.
Nothing good can come from insisting you're alpha or beta or sigma or whatever the hell else. Your self-talk matters yes, but it's pointless to describe yourself in such a reductionistic way and think that's all you are.