Being you isn't being a person. All your experiences, desires, actions, and beliefs create you. You are a sum of those things. If you get a heart transplant you are still you. But if you got a memory transplant would you still be you?
Water isn't something that has oxygen and hydrogen added to it. Hydrogen and oxygen combined create water. Water doesn't really exist. Likewise you are a combination of experiences and events combined to make you. But then does that make you non-existential?
We do exist. Compare us to a waterfall. The waterfall is in a way permanent, yet not. Water will continue carving new paths and creating more life, and the water itself is different every single instant. The waterfall is still very real. The real you is always changing as well and, therefore, exists.
By trying to discover your true self you will realize that there is several "yous" that you've experienced. All the "yous" are tied together by already experienced history.
The real you isn't inside, it's outside of you. And when you attempt to find your true self you invariably will create part of it.