Hi, checkerboard. Great question! 🙂
Depending on your familiarity with WooCommerce and The Events Calendar, you could certainly create some logic to label tickets on the emails. Unfortunately, for most users this would be a bit of a heavy lift, so to speak. The simplest solution is probably to advise your client to label the tickets with the event name or something that will identify it to them when they receive the emails.
A list of attendees is available from each (backend) event page in TEC. There is currently no place with a consolidated view of all tickets purchased for all events.
Happy holidays!