Do it the easy way:
Change your Apple ID - https://support.apple.com/HT202667 - "Follow these steps to change the email address that you use as your Apple ID." Plus special instructions if you want to change your Apple ID to an @icloud.com address. You may also wish to turn off "Find My" before changing information and turn it on again afterward.
"After you change your Apple ID email address or password, you might need to update your sign-in information with any Apple services you're using" Click on this link to read "What to do after [or before] you change your Apple ID email address or password" --> https://support.apple.com/HT204071