Oftentimes, it is because of discrimination that still exists today. For example, JK Rowling used the letters JK instead of Joanne because it was said that if people knew from the start that she was a woman, people would have been less interested in reading her books. Also, the same has been done by Jewish people, and other groups that have been discriminated against in history.
Sometimes though, people just think that a name sounds better than their name. It is similar to an AIM name that you create. not everyone wants their screen name to be their real name.