Are you the clothes you wear? No you are not. In a similar manner - your personality is what you show to the world. A construct based as a response to some trauma (or something else very influential, but usually trauma) inflicted on you as a child. i.e. your personality is the clothes your real self wears. It doesn't mean it's not part of you - it is.
I am not the clothes I wear, but personality is not "clothes." If personality were clothing then removing it would be a simple and painless matter, after which you would be interacting with the world "without personality." This is absurd. You can't have no personality. All you can do is replace a personality with a different personality. Your personality is the totality of patterns by which you present yourself to the world.
This is not the same thing as what you show to the world. "What you show to the world" implies that personality is merely a veil that covers stuff. It's not a veil at all. It's an interface. The "real you" that acts through this interface is beyond words, personality is not "showing it" because it can't be shown, but rather mediating it via actions.
Some of my language patterns come from watching and interacting with my stepfather. He was big man with a loud voice and an iron work ethic. I didn't get along with him when I was a kid-- in fact had to leave home after threatening his life-- but as I became a man I decided that I was going to force the world NOT TO IGNORE ME. So I tried on his tough-talking, Navy veteran persona and found that it fit me. Now I'm 275 pounds and have a loud voice and I know how to use it.
I'm not PRETENDING to be something I'm not. I am using a style of interaction that fits the "real me." I AM a man, and I SPEAK as a man. And my template for manliness is my stepfather. At the same time I'm also an intellectual, and I adopted certain patterns from my biological father. I also borrowed patterns from the writings of C.S. Lewis and Tolkein. Sometimes I channel Gandalf and sometimes Boromir.
Children have become adults in this way since a million years ago. There's nothing false about it.
This makes it sound like our personalities are a function of our own agency. What about genetics?
I agree that our personalities are partly a function of our past lives (trauma as you say), but that's only part of the picture surely.