All 406 MHz emergency beacon owners/operators should register their 406 MHz emergency beacon (ELTs, PLBs and EPIRBs). Registration information is vital to Search and Rescue (SAR) services while prosecuting SAR cases; it is to your benefit to have a registered beacon in the event of a distress.
All vessels under the SOLAS convention and aircraft operating under the ICAO regulations must register their beacons. Some national Administrations also require registration of 406 MHz beacons.
Document C/S S.007 "Cospas-Sarsat Handbook of Beacon Regulations" provides the status of 406 MHz beacon regulations in specific countries and extracts of some international regulations pertaining to 406 MHz beacons. You may also wish to check with your local search and rescue or maritime/aviation transportation authorities for further details.