Adding Organization filter to Event details report
"Simple" is a relative term here!  This is an excellent beginner-level modification to CiviCRM's source code - but any modification requires a fair amount of knowledge.

Assuming you're using the "Current Employer" as the organization name, you're in luck.  The current employer's name is stored in the "Organization Name" field on the individual's contact.

You'll need to modify the file in CRM/Report/Form/Event/ParticipantListing.php.  Check out this session from CiviCon 2012 for a video and slides.

While it's not suitable as a learning resource, the CiviReport Reference is an excellent reference document.