You are wrong. The term "Jew" has been universally applied to all Israel since the days of Ezra. Ask any Cohen or Levi today (both are from the Tribe of Levi, not Judah). They'll identify as Jews, and every Jew on the planet would recognize them as such. Heck, consult your Christian Bible. Paul was from the Tribe of Benjamin. But he clearly identifies as a Jew.
I once asked a Jewish acquaintance if there were any identifiable remnants left today of the Tribe of Dan -- there is some reason to believe that they were Danuna (Egyptian name for them, the Phoenicians called them dynnm), identifiable with the Greek Danawoi, or "Danaans", who were the actual people who brought the Greek language from the steppes of Russia to the land of Hellas. Moreover, out on the steppe, they may have been the enemy people identified by the Vedic hymns as the Danawo.
If so, then these Danaans are mentioned in the Vedas, are the authors of Greek civilization and are prime actors in the Iliad and Odyssey, had their images and their names carved in the Ramessid monuments of Egypt, and came at last to the Bible as the Tribe of Dan -- certainly the most spectacularly rich patrimony of any identifiable people on earth.