A rather difficult and undocumented feature which turns out to be a very simple thing to do it changing the sent from name on an Apple Custom Email Domain.

After adding your domain to your iCloud account, go to the mail app via a web browser. At the top left, click the gear icon and select preferences.

On the left, select Accounts and select the custom domain email for which you want to set the name and enter it into the Full name input. Click close and you're set!

Note: I have noticed that sending an email from your iPhone using a custom email domain will still send the From as your Apple ID name. If you want to make sure this does not happen, send the emails from a web browser from: https://www.icloud.com/mail/