How would an individual during the Viking invasions identify a Norseman as Dane, or Norwegian? Was there any reason as to why such a distinction would be important?

I would like to try and answer your question, but i need some clarification, because it is actually a pretty tricky question. Do you mean how other europeans would perceive them? Or how they would identify each other when they often met? Because danes, norwegians and swedes didnt necessarily visit the same locations.