/etc/mailname:
domain.com

/etc/exim4/update-exim4.conf.conf :
dc_eximconfig_configtype='internet'
dc_other_hostnames='domain.org'
dc_local_interfaces=''
dc_readhost=''
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets='192.168.1.0/24'
dc_smarthost=''
CFILEMODE='644'
dc_use_split_config='false'
dc_hide_mailname=''
dc_mailname_in_oh='true'
dc_localdelivery=maildir_home