Changing an Apple ID from one @icloud.com address to another

Solution 1:

From the Apple Support page about changing your Apple ID (emphasis added by me):

If your Apple ID email address ends with @icloud.com, @me.com, or @mac.com, you can only change your email address to another @icloud.com, @me.com, or @mac.com email that's already associated with your account.

https://support.apple.com/en-us/HT202667

If you created your Apple ID recently with an @icloud.com address as identifier, you most probably can't change that. I think the support document I linked to is targeted at users who have old @me.com or @mac.com addresses that Apple used to issue a long while ago. Or maybe there could be special situations where you actually have two @icloud.com addresses associated with one Apple ID as the result of merging two IDs with the help of Apple Support, but those would be rare exceptional cases. For a recently created @icloud.com style Apple ID, typically you can't change it.

Solution 2:

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.