Attempting to set up an exim4 SMTP only server that can send out messages from two domains

Question

I am attempting to set a STMP server that can send out messages from two different domains

Adding this line to the the config file (update-exim4.conf.conf)

PRIMARY_HOSTNAME = $sender_address_domain

Gave the follow header:

Received: from [...] (helo=name)

By MAIN_HARDCODE_$sender_address_domain with esmtp (Exim 4.96) (envelope-from [email protected])

I want something like this:

By exsamplemail.com with esmtp (Exim 4.96)

I am on Debian 12