Just to confirm Gil's response - YES - a separate registration for each device.
Each device has its own Beacon ID, thus it has its own registration. If not, imagine the chaos that would ensue if you were out flying in your 406 ELT-equipped airplane and your wife had borrowed your PLB to go hiking. How would the Rescue Coordination Center know which person/device was in need of help? Once registration per device is the simple solution.
Please ensure you use current, accurate contact info in the registration - after all, that's what's going to be used to try to find you via a communications search.