I've named myself the names I like. And depending on the sex I choose for my character, of course.
Although, in White 2 I named myself my real name. And to be honest, I did like the experience. But, I prefer using other names that I like more than my real name.
Some of my more recent names include Cody, William, Sophie, Tente, among others. I think I'll do Peter next. Or Maanasa, if I choose female. (From the trailer, it appears the female is Caucasian/Japanese but I don't caaaaaaaaare~.)