How to change iCloud email after surname change?

You can change the part preceding the @iCloud.com portion of your email address only on an iOS or iPadOS device running iOS or iPadOS 18.1 or later.

Go to Settings ➜ Account ➜ Sign in & Security ➜ Select your iCloud address ➜ and then click on Change Email Address.

I would not suggest this option as any thing that is still using the old address will no longer arrive in your inbox. This basically cancels the account so any body that sends an email to that address will just get an error back. This also requires you to update any services you may be logged in to with that address to the new one to continue to receive email to you iCloud account. It is just a lot of trouble.

Another option is to simply create an alias with the new name and use that to start emails you send now instead of the original email address.

click here ➜ Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

Or even more simply, change the display name for the account. While the actual address remains the same the "From" name other people see can be modified by altering the Name in the "My Card" entry in the contacts App on any iOS device or Mac.

Apple's online information about how to do this is confusing. Try the method below. If that doesn't work, using an alias instead.

Change your Apple Account primary email address - Apple Support

“You can change your iCloud email address using a device with iOS 18.1 or later, and iPadOS 18.1 or later.”

Create a primary email address for iCloud Mail - Apple Support

Note: You can’t rename your primary iCloud Mail email address later. If you change your mind, you can add an email alias instead.