Your "real name" is what appears beside all of your submissions and in your public CBC profile.
When you register using Facebook or Google, your real name is the same as the name that appears on those social networks. The only way to change your real name when you register with Facebook or Google is to change it on the social network site.
When you register using an email address, you will be asked to provide a real name, which will appear on all your submissions to CBC.ca. You can change your name by accessing your CBC profile.