First enable the Provisioning API for your Google Apps account.
Download and extract Google Apps Manager (gam.exe).
Open a DOS box and get your domain info:
gam.exe info domain
Change your Google Apps username by using the update parameter:
gam update user <olduser> username <newuser>
As you can see in the screenshot above I didn’t got any information from gam.exe. But when signing in to my Google account was only possible with the new user. Thanks Google Apps Manager!
To clean things up, I disabled the Provisioning API again.