Host of the 1994 Winter Olympic Games, Lillehammer, Norway, has a much easier name to track down than Nagano, Japan. According to Wikipedia Lillehammer was named after the old Hamar farm that was already there when the town was established on January 1, 1838. There was a slight problem, though, there was another town called Hamar close by, so the town became known as Lilþlæ Hamar or Litlihamarr, which means “little hamar,” and eventually that was shortened and modernized to Lillehammer.
Interestingly, Lillehammer has the only coat of arms, (pictured here), with the image of a skier on it.