To indicate the message recipient, an email address may have an associated display name for the recipient, which is followed by the address specification surrounded by angled brackets, e.g.:
John Smith <john.smith@example.org>
In the example above the display name is John Smith.
Setting the display name for a normal Gmail account is easy, but how to set the display name for a Google Apps email alias?
I see no way to configure it when creating an alias:
Best Answer
After you create your alias through Admin Console then you have to set it up as a sender in your Gmail settings.
Gmail Mailbox > Gear icon > Settings > Accounts > Send Mail as : Add another email address that you own
You put the display name you want, you enter the alias you created through Admin Console (someuser@gmail.com), you leave checked the "Treat as an alias" box and you are ready to go.