how to change notification email without changing apple id

From: About your Apple ID email addresses - Apple Support

Add or change a rescue [for most people called a notification address] email address

1. Sign in to appleid.apple.com.

2. Select Sign-In and Security.

3. Select Rescue Email. You might be asked to answer one or more security questions or enter your Apple ID password before you continue.

4. To add a rescue email address, select Add email. Then enter your rescue email address, then select Save changes. We send a verification to that address.

5. To change a rescue email address, enter the new address. We send a verification to that address.

6. Enter the verification code and click Continue.

If at any stage you don't get an expected verification see: If you didn't receive your verification or reset email - Apple Support

If you had a rescue email address on file when you upgraded to two-factor authentication or two-step verification, that email becomes your notification email. You can also use these steps to edit your notification email address. If you remove the notification email, you won't be able to add a new one.