On all sites but Cooking.SE, I'm (my user is) GUI-Junkie. On the UX.SE chat, I'm BaffledCook.
What exactly is the bug? I believe your chat username is based on what account is set as the parent user. You have the most reputation on cooking, so it must have chosen that one.
If you open up any chat and click your username you can see the parent user listed on your profile and change it to an account that has GUI Junkie as the username.