It's fine, sweetie. It is like two separate personalities, actually, trying to blend into one. And it bothered me a great deal in the beginning. Some days it still does.
For a while, I tried to keep River separate, pretend she was someone else, but she isn't. I tried calling it a past life, but it isn't quite that either. I'm as much River as I am Melody. More one or the other at any given moment, but always both.