If a domain has an “owned” IP, it would be possible to also get exim to show a unique banner for that IP. You can accomplish this by edint the /etc/exim.conf and adding the following code into the top section of the exim.conf.
smtp_banner =\
${if and{\
{def:interface_address}\
{eq{${interface_address}}{1.2.3.4}}\
} {mail.host1.com}{mail.host2.com}} ESMTP $tod_full
In the above example, any connections to 1.2.3.4 will show mail.host1.com as the greeting hostname, whilte all other connection to port 25 will show mail.host.com.