[exim] Multiple exim hostnames under WHM/cPanel

Greetings list,

We're running exim under WHM/cPanel and would like to change the HELO/welcome
message presented by Exim based on which IP address it is contacted on.

if an email is sent to example1.com, exim currently answers with:

220-name.example1.com ESMTP Exim 4.52 #1 Sat, 09 Dec 2006 06:17:16 +0400
220-We do not authorize the use of this system to transport unsolicited,
220 and/or bulk e-mail.

However, if the email is to be sent to example2.com which is on a separate,
dedicated IP address with a different MX record, the Exim system still
replies with the above 220-name.exxample1.com instead of:

220-yalla.example2.com ESMTP Exim 4.52 #1 Sat, 09 Dec 2006 06:17:16 +0400
220-We do not authorize the use of this system to transport unsolicited,
220 and/or bulk e-mail.

I assume the problem lies in here in the top of the exim configuration, as the
WHM/cpanel system has one hostname for all the IP addresses we've bought:

# Specify your host's canonical name here. This should normally be the fully
# qualified "official" name of your host. If this option is not set, the
# uname() function is called to obtain the name.

Is there anything I can replace this with, so that it checks what IP address
it is being contacted on, and based on that change the hostname in the
220-messages?

Thanks in advance!