Just to aid future searchers...
To change the name used when zimbra sends HELO to a remote system do
postconf -e smtp_helo_name = 'collaboration.somedomain.com'
To change the name used to greet remote systems (i.e., when you telnet to port 25 on the zimbra server), do this:
postconf -e smtpd_banner = '$smtp_helo_name ESMTP $mail_name'
I have it greet with whatever name it's going to use when sending out mail.
In both cases in order to make the change permanent across upgrades the wiki says to do
zmlocalconfig -e postfix_smtp_helo_name = 'collaboration.somedomain.com'
zmlocalconfig -e postfix_smtpd_banner = '$smtp_helo_name ESMTP $mail_name'