Norway is a “first to file” jurisdiction, so registration is mandatory to obtain rights over a trademark. Only in exceptional cases can unregistered trademarks be protected, and then only when they have been extensively used.
Trademark applications must be filed with the Norwegian Industrial Property Office PATENTSTYRET. A Norwegian trademark registration also covers Svalbard and Jan Mayen.
It is not necessary for the trademark to be in use in Norway in order for it to register. However, prior use can be helpful, as it may serve to overcome objections based on lack of distinctiveness by proving that the trademark has acquired distinctiveness through use.
If you register a combined trademark (containing both word and figurative elements) in Norway, the exclusive right is limited to the exact configuration in which it was filed and registered. If you want to use the word element separately from the logo (or vice versa), it is advisable to file an additional application for a mark that includes only the elements you wish to use and protect independently.