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The only people who can do this are the Hosts, and they will only do it when the username in question poses a security risk, for example someone giving their real name and then realising they didn't want to. Since I would doubt this applies in your case your easiest bet is to obtain a free email account from Yahoo or similar and create an Apple ID using that. Then you can create a new ASC account with the screen name of your choice and ignore the old one. Since the ID address will be used as a contact address should the Hosts ever need to contact you, you could set up forwarding from it to your normal address (provided the supplier allows this - most do).

Having created a new ID you will have to sign out of your current ASC account. Then go to the 'welcome' page, http://discussions.apple.com and sign in with the new ID. As this is a new account you will be asked to create a profile.

If you logged in state is "Guest", you can choose "Login" from any page > then "Create New Account" from the left side of the resulting page (where you login every time)