When you create an Apple ID you can either (1) sign up by using a third party email address or (2) choose to create an iCloud email address and sign up by using that iCloud email address.
If you choose option (1), your Apple ID/iCloud account will initially not have an iCloud email address associated with it at all. The third party email address you use to sign up will be your Apple ID's name (and also the primary way Apple will contact you; for example to confirm App Store purchases). You will be able to use other iCloud services such as Find My iPhone, Notes and Reminders. Just no iCloud email. It is still possible to create an iCloud email address for that Apple ID at any time after you initially signed up by using your third party email. This can be done in the Settings app on iOS or MacOS or by clicking on the email icon on iCloud.com. You will however not be able to change your Apple ID's name from the third party email address you used upon signup to your newly created iCloud email address. Your Apple ID's name can only be changed to another third party email that is not already in use by another Apple ID.
As such, unfortunately currently it is not possible to change an Apple ID's name/primary email from a third party email address to an iCloud email address (i.e. to the same iCloud email address that is already associated with/an alias for that Apple ID).
This is a known issue and it has been known for a very long time. From a user perspective, its completely insane.
The topic is extensively discussed in this thread https://discussions.apple.com/thread/4434456.
I strongly encourage you to provide feedback to Apple as indicated in this post https://discussions.apple.com/thread/4434456?answerId=32026857022#32026857022.
If you choose option (2) upon sign up however, your newly created iCloud email address will be your Apple ID's name and your Apple ID's name cannot be changed at all. This option is only available when an Apple ID is created on iOS or MacOS through the Settings app or through the device setup menu.
