How to change display name on the iCloud email?
After logging in to iCloud.com, click Mail, and then at the bottom-left of the screen click on the Settings (gear) icon. Click Preferences... in the pop-up menu. In the pop-up window, click Accounts then change Full Name to how you'd like your name to appear.

This will change the name that appears on emails you send through the iCloud.com website and the Mail app on OS X. If you are using another desktop mail client, you will need to configure that separately.