The logical hostname need not be related to the name returned by the hostname command, nor need it be the name returned from a reverse lookup of the host's IP address.
The logical hostname need not be related to the domains hosted.
The logical hostname is selected at install time, and is configured in the LDAP server at that time.
The logical hostname can be determined by running the zmhostname command.
Changing the logical hostname is a pain.
The following requirements for the logical hostname should be met: