Add new email address in iCloud

See the article About your Apple ID email addresses - Apple Support

Additional email addresses

Many of us have more than one email address that friends and family use to reach us. You can add additional Reachable At email addresses that you commonly use to your Apple ID account, so people can easily find and communicate with you on Apple services like FaceTime, Messages, Shared Albums, and Find My, and collaborate with Pages, Numbers, and Keynote.

Add an additional email address

1. Sign in to appleid.apple.com.
2. Select Personal Information.
3. Choose Reachable At, then select the Add button .
4. Enter your additional email address. Make sure that you're not already using it as an Apple ID. 
5. We'll send a verification to that address. Didn't get the email?
6. Enter the verification code and select Continue.