Can you still create an Apple ID with a name that's not an e-mail address?
It a not possible to create a non-email address Apple ID any longer. 

As a matter of fact, they are becoming more and more inconvenient, as various Apple services begin to assume that your Apple ID is an email. If you have not started to notice it yet, trust me, you will, soon.

I recently changed my non-email Apple ID to the linked email address. You can change the username of an Apple ID without starting a new account.