Mails from my system are being rejected when the receiving server does HELO checking. I believe my system is sending the wrong domain name. I'm running exim4. Googling for anything about exim4 and domains yields a nightmarish list of irrelevant results. Similarly, googling for HELO rejections yields a horde of outlook users who need to turn on SMTP authentication. I cannot for the life of me figure out this simple question: which hostname is exim sending and how do I change it?
Unfortunately, I can't watch what exim is sending over the wire, so I have no way to debug this myself. I'm hoping someone has had this problem and just knows :).