As a general rule, modern Norwegian does not use exonyms for names with endonyms in Latin script.
Until recently, most people tended to use the official Swedish names in Norwegian.
In recent years, however, the use of Finnish place names have gained some popularity in Norwegian.
Newspapers in Norway often, but absolutely not always, write all ä as æ (sometimes e) and all ö as ø, probably because ä and ö were historically lacking on Norwegian typewriters.
Some places have genuine Norwegian names because they were originally part of Norway: