Are you doing it this way?
Here's how you change the email address (Apple ID) you use for your Apple Account while retaining everything in your account:
1. Go to https://appleid.apple.com and sign in.
2. In the Sign-In and Security section, choose Apple ID.
3. Enter the email address that you want to use as your Apple ID.
4. Choose Change Apple ID.
5. If you changed your Apple ID to a third-party email address, check your email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support
6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support
For more details, read the document: "Change your Apple ID" --> Change your Apple ID - Apple Support
To change a notification email address:
On the https://appleid.apple.com/account/manage page, scroll down to the security section. Then, click the edit option. When you do, you will see an option for the notification email.
If you are, and you are having problems, you will need to describe those in more detail. We only know what you tell us.