If you want to get rid of "On behalf of" in your headers you need to set "Set SMTP Sender: headers" to off from the inside your Exim configuration
WHM –> Service Configuration –> Exim Configuration Manager –> Set SMTP Sender: headers
Should be OFF
grep local_from_check /etc/exim.conf.local
There is shouldn't be any output
Otherwise remove local_from_check from the /etc/exim.conf.local
/scripts/buildeximconf /scripts/restartsrv_exim