I have quite a few agents that run on schedule and send mails - what I did was to create a user named 'Automated Message/<mydomain>', add them to the ACL of the databases as well as the security section of the server docs, and finally to the 'Run on behalf of' field of my agents.
Then when the agent runs, it is sent from 'Automated message' - no confusion.
You could create a similar user (no Notes ID needed) and make the primary email address 'no.reply@xxxx.com'