Because "Northern Lights Inn" was the best known of many names it had throughout its history, or at the very least the one that stuck.  It was called the Ramada when Mike Cusack took it and the Polaris in Fairbanks and started claiming they were a hotel chain.  "Northern Lights Hotel" was the name of that "chain" and the last name it operated under when the whole venture suddenly went belly-up.  That's why the signs with that name were still up all those years later;  that was certainly the case with the Polaris.