I'm afraid you can't do that. You can change your ID to another non-Apple address which isn't currently or recently associated with another Apple ID, but you cannot change it to any @icloud.com, @me.com or @mac.com address. (Apparently the address you give is the main iCloud address, not actually an alias - aliases are additional iCloud addresses, but the same thing applies - they can't be moved to another account or turned into an ID.)
In your situation you should certainly change your ID to a functioning address. To do this please follow the following process:
- Firstly, sign out of iCloud on all your devices: go to each of your devices and sign out in System Preferences (or Settings)>iCloud - 'Sign out' on a Mac, 'Delete this account' on an iOS device (this will not delete the account from the server). If you have 'Find My iPhone' etc enabled you will need to disable it first. Your synced data will disappear from your devices but will reappear when you sign back in.
- Create a new email address, for example at Yahoo or Gmail, or anywhere convenient (or you can use an existing address as long as it is not associated with an Apple ID).
- Go to http://appleid.apple.com and click 'Manage your Apple ID'. Sign in with the current ID.
- Where it says 'Apple ID and primary email address' and gives your current ID email address, click 'edit'.
- Enter your new address and click 'Save changes'
- Sign back into iCloud on all your devices with the new ID and password. Your synced data will reappear (give it time).
I reiterate - before you start, sign out of iCloud on all your devices. Failure to do this will lead you into difficulties.
