This is how I configure delivery of e-mail generated on “sattelite” machines.
On SMTP relaying server, edit /etc/postfix/helo_access:
# postmap helo_access
a_random_name_known_by_server_and_client1_only PERMIT
a_random_name_known_by_server_and_client2_only PERMIT
...
To update the database file format used by postfix, run postmap helo_access. The main.cf file must then specify:
smtpd_recipient_restrictions =
permit_mynetworks
check_helo_access hash:/etc/postfix/helo_access
...
On each “clientX” or sattelite system, specify myhostname as a_random_name… reload/restart postfix, and everything should be up and running.