Introduction The Sender header is described in the RFC here: https://tools.ietf.org/html/rfc4021#section-2.1.3 2.1.3. Header Field: SenderDescription: Mailbox of message sender [...] Related in...
Can you check that setting to see if that is the behavior you're looking for?
As for a full custom header, I didn't find much documentation out there for that, and a few of my own tests with exim.conf did not cause the additional headers to be displayed when sending to a service like Gmail. It might be a good thing to ask the Exim Users List to see if that is possible to apply it to all messages sent from the system.