If you're in S/4HANA, I believe there are some new features (finally) in the output. I don't have the details but just heard it mentioned in some presentation.
In ECC, this should be covered by the existing posts from the last decade. Try Google -> "billing document email output subject PDF file name site:sap.com". There are rather limited options.
That's true but many companies use (used) standard output programs with custom forms. I wouldn't advise creating a Z copy of a print program (because then you won't get any support from SAP for it) just because of the email subject/file name. Unless it's of tremendous importance, which I seriously doubt.