You can set an "email from" in either the automation/notification or an Emailer transformer. The actual hostname/ip address of the actual FME Server is visible in the email headers, but most users won't dig that deep.

Thank you @Hans van der Maarel​ ,

but I can't view that information because I can't send the e-mail message. In my configuration FME Server has to use an smtp relay to deliver messages and I suspect it sends the messages as localhost instead from the correct domain. If the sending hostname is written in some configuration files, I could try do debug the problem.

Right. The hostname is what's visible in your browser's address bar. Alternatively you can check the $FME_SERVER_HOST parameter (set up a workspace that logs that parameter value and then run it on FME Server).

If your FME Server was installed with "localhost" as hostname then you may indeed be in trouble. It can only be changed through a re-install (see this idea)