From 1 January 2020, it is allowed to have one or more citizenships in addition to a Norwegian citizenship. You can have one or more citizenships in addition to a Norwegian citizenship.
Even so, if the country you are a citizen of now does not allow that you have more than one citizenship, you can still lose this citizenship when you become a Norwegian citizen. You must make sure what the rules are in the country you are now a citizen of. You can for example look for information on an official website which belongs to the authorities in this country or ask an embassy.
You do not have to inform Norwegian authorities that you wish to keep your previous citizenship.
In principle, as a Norwegian citizen, you are obliged to serve your military service in Norway, but the rules vary depending on which other country you are a citizen of. If you have questions about military service, you can contact the Norwegian Armed Forces (external website).