I think a great way to make this easier would be to show the profile picture of the admin user at this place. Also I think the standard CiviCRM logo should adhere to the "Show 'powered by' setting" in civicrm/admin/setting/misc I will create a PR for the later option.
I wrote an extension to do this called altinvoice. You can set relationship types to receive a copy of the invoice. E.g. "When I invoice this organization, also send a copy to anyone with the relationship type of 'Billing Contact' or 'Site Coordinator'".