This prob­lem annoys the heck out of me, and appar­ently thou­sands of other Solaris admins. I can't imag­ine the rea­son some­one thought send­mail should log this error every few min­utes about the stu­pid host­name, but must have been a good one because the app sure is adamant about it.

1. Type /usr/lib/mail/sh/check-hostname and fol­low the sug­ges­tions
2. Become root
3. chmod 644 /etc/inet/hosts
4. vim /etc/inet/hosts (or edit with any other text-program) and
change the hosts file as /usr/lib/mail/sh/check-hostname sug­gests.
5. Save the changes
6. chmod 444 /etc/inet/hosts

tldr Add "fully-qualified" name in /etc/hosts — so add myserver.fakedomain.com to shut it up