Reading this topic really helped me. I've been dealing with the same feelings of being fake, at near 5 months into HRT. Usually I do pretty well, but when I am switching between gender roles (presenting as male at my jobs for the moment), it really throws me off. I get dysphoric at work, then feel fake when I do present as a girl. I'm not used to my name 100% yet either, and the awkwardness of going through puberty just makes things feel fake.
I think about if I'm making the right choice, but then imagined myself going back to a male body, and I literally cringed multiple times at the thought. So that just makes it clear to me to keep going despite those feelings. I think it is a lot of adapting to a new role. It may be how you identify, but nonetheless we learn a lot about that role when we finally do enter it, and feel really out of place until we can adjust.
Sorry if this sounds weird, I'm sleepy at 3am and am not the most organized in thought. 😛