How can I change my email address that Apple uses to communicate with me?

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

Or if you mean this:

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