From 21 December 2020, all travelers entering Norway are required to register their name, contact details, place of quarantine, employer (if applicable) and any other information requested. The purpose of registration is to ensure compliance with the quarantine requirements, enhance infection control and promote more effective contact tracing.
The registration form must be filled in prior to arrival in Norway, and be handed in to the police at the border control. The registration form can be found here: https://www.regjeringen.no/en/topics/koronavirus-covid-19/self-declaration-form-for-persons-who-are-to-undergo-entry-quarantine/id2791503/
More information about the registration requirement can be found at the website of the Norwegian Government: https://www.regjeringen.no/en/aktuelt/government-introduced-registration-requirement-for-all-people-entering-norway/id2815594/