If you mean the sending name that appears on the "From:" line, to change it on and iOS device, go to Settings>Mail,Contacts,Calendars...tap iCloud under Accounts, tap your iCloud account at the top of the next screen, tap Mail at the bottom of the next screen, then enter the name you want to use in the Name field at the top.
To change the From name on your Mac Mail, go to icloud.com, sign into your account, open Mail, click the gear shaped icon on the bottom left and choose Preferences, go to the Accounts tab and enter the name you want to use in the Full Name field and click Done. Then quit Mail on your Mac and re-open it. Your new From name should now appear in the drop-down list when you compose a new email.