The specific tribe name is preferred over any group name—and then as you say Indigenous Americans or Amerixan Indians; Native American is a white term is my understanding. (My university sits partially on land previously held by several Indigenous tribes, and there’s a statement on every university website acknowledging this—the tribes are identified each by name.)

In the case of the original Thanksgiving, the tribe is the Wampanoag tribe. And, actually, the story of the first Thanksgiving goes even deeper (I teach it in a survey class of world folklore I sometimes do). “Thanksgiving” actually refers not to a harvest festival, but a war victory, and the name comes from an 1863 proclamation celebrating Civil War Union victories at Gettysburg and Vicksburg.

It wasn’t the first harvest festival celebrated in the New World, and the Wampanoag were actually trying to make an alliance with Plymouth (some sources suggest they actually gate-crashed the Plymouth harvest festival, they weren’t invited).

And there was no turkey, no pie, and no potatoes. Most of what we celebrate as Thanksgiving is late-19th century tradition.