The username is that which you login with (along with your password). Once you have registered it, you are unable to change it afterwards. 

Your real name is the field where you put in your actual full and real name. Don't worry, this will not be visible to other members. 

Your Display Name, however, is the name that you will appear as for yourself and other members. It can be the same as your username, but doesn't have to be. You can change it as many times as you like. Unlike your username, your Display Name can contain spaces and special characters.