Changing how you behave isn't fake, it's just unfamiliar
Most people have the misconception that our personality is set in stone since birth and that changing it is inauthentic and fake. This isn't true.
Lots of people have the misconception that if you change your behavior, the way you act, that you are being inauthentic to your "true self".
However, this is not true.
What is your true self?
For the most part, it's the culmination of years of experience - your mind was shaped by your experiences and how you reacted. It was then reinforced and solidified with the ending result being you and your behavior.
Just like learning an instrument or any other skills, you are completely inept in the beginning. But does that mean you are faking it?
Are you faking being a musician for practicing it? Are you faking being an actor for acting?
I would argue no. Maybe by some arbitrary standard, you haven't received public recognition for your competence yet, but I would argue that you are the very thing you do.
You are what you do.
So fake it till you make it.
Done repeatedly enough, you will truly become that "thing".
How to change yourself
For example, right now you could be the least socially capable person in the room, unable to strike up a conversation with anyone.
But if you hammer it enough and force yourself to talk to literally everyone, doing this repeatedly every time and at every occasion, then there will come a day where you are objectively the most social person in the room. Everyone's opinion of you will change too. You will be the social butterfly.
Now is that the "true you"? Are you just faking it?
We aren't born out of the womb in a set way. You don't come out having these social skills. Of course you may have some predispositions, but they are slight and unimportant.
What is important is our ability to change and become the thing we do.
We can quite literally change our identity in any field with enough persistent effort.
So just because it feels uncomfortable in the beginning, doesn't mean that you are being inauthentic and faking it. It just means that it is unfamiliar! It's a totally normal feeling that is experienced every time we undertake doing something new. So embrace the feeling.
TLDR
We are not being fake for trying to change our behavior - the feeling we have is unfamiliar not inauthenticity. We become what we do.