If you say that you have an account but no username, that means that you're connected to Youtube by your email (gmail,hotmail,etc) or that you don't actually have an account and you're just a visitor. Log out of your email account (it'll be in *settings*) and then sign up into a real account.
You actually create a YouTube username the same way you do with any other website registration. You must consider creating a YouTube username that entirely protects your anonymity. Check out windmillnetworking.com/2010/01/11/youtube-advice-for-beginners-the-importance-of-your-username/ for more information.