By default Exim4 presents the system hostname as the HELO greeting during an SMTP session. If you are using the Debian Exim with the “single file config” and want to define a specific hostname to use, create the following file containing the line below:
primary_hostname = my.server.fqdn.net
Restart Exim for the change to take effect.
This local configuration file will not get overwritten with software updates.
Test immediately after making changes and examine logs to verify operation is as expected.