As of Aug, 2019, the situation is still unresolved.
After a conversation with Apple Support it transpired that the ability to change an AppleID that ends with @icloud.com to a mail alias that end in @icloud.com is not implemented.
However, it is possible to do this if your mail alias end in @me.com or @mac.com, which is what the support article mentioned in the accepted answer refers to.
Apparently, the reason this hasn't been implemented is because this feature hasn't been requested often enough by the users.
If you're affected by this, or if you would like to see this implemented, please visit https://www.apple.com/feedback/icloud.html (Feedback Type: Account) and submit the feedback form to let Apple know that you too would like this feature implemented.