Do I need to change log-in user name for Apple ID when I have changed to new email service and deleted the old email account?

I suggest you change your ID to a working email address so you can receive information related to your Apple ID. For example,  if you forget your password, you can't access your email to get emails from Apple to recover your account

Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

This has been corrected. Thanks