This is normal behavior, just a quirk of the forum software that occasionally causes confusion.
What you see when you are logged in is not what other people see. When you are logged in, you see your real name on your activity. Other users will see your user name. You can test this by logging out, and then going back to look at your own posts. You should see your user name, not your real name.
Who sees your real name is controlled in your privacy settings. See: What about privacy? Who can see what about me?