I want to change my maiden name to my married name that is associated with my iCloud email

You cannot change the part before the @ in your iCloud email address as that would make it an entirely new account.

You can change the name associated with your account that is used as the sender name for iCloud email from the Apple ID settings on your device or at https://appleid.apple.com

You can create an alias on your iCloud account with your married name if you wish, and use that to send and receive email instead.