I'm going to offer a different perspective. And some of you may disagree, but this is my opinion.
It's just a name. It's not a big deal. It doesn't change who you are.
I was born in South Korea, and was given a male Korean name at birth. When I moved to the United States, I kept my Korean name. It was difficult for my friends to pronounce, but they got used to it.
Just before I started college, I thought it might be helpful to have a more common American name, anticipating all the new friends I would meet. So I legally change my name from a male Korean name to a male American name.
Many years later, when I first started going out into the real-world TG community, I chose the name "Mirya" for myself, because I thought it was pretty and unique. (it also happened to be the name of my primary World of Warcraft character, and I'm a huge gaming nerd!).
Eventually when my transition progressed to the point where it came time for me to do my legal name change, I decided I wanted a more common first name in order to make things easier when meeting new people. So I chose Emily. And I made Mirya into my middle name.
Now I am thinking about what kind of name I want to have as my female Korean name. I settled on 은비 (pronounced Eun Bee in English), which means "Silver Rain".
So as you can see, I have gone through many different names and changed my legal name twice (once as a guy, and once as a girl!) Through it all, I never felt anything weird or special about each name change. Again, it's just a name. It doesn't change who I am. It doesn't define who I am.