Update the user name when user's email is changed

First, thank you for this module. I like that it removes an extra field (user name) for users to remember by forcing a portion of the email, or in my case, the entire email to be the user name.

The problem I'm having is when a user clicks on the user edit form. Changing the email address here does not automatically update the user name and I think that creates a lot of confusion. If I change the administration settings to allow users to change their user name, than the user edit form displays both a user name and email address fields which add more confusion. Is there a way to force the same logic on the user edit form as in the user registration form where a change on the email results on a change to the user name based on what is returned from hook_email_registration_name()

Thanks