Dude! What's with the past tense? The answer is yes. We identify by our nations! And since we've been placed in a group and treated as a group by governments, we organize and fight back as a larger group. Languages such as Nuxalk, Cree, Tsimshian, all developed words to mean "everyone not white", ie Indian and they included themselves in that category, but our own nations always remained more prominent to our identity, just as your siblings are more important to you than your continent Or nation in terms of identity
I know this might not be the right sub for my follow-up question, but here it goes.
I guess a lot of people who are either full-blooded or part native Americans today, are quite proud of their heritage. Do they distinguish between different tribes? Would someone call themselves half Sioux or half indian?
Identity can be considered at many scales, and more than one at a time may apply. On the one, I consider myself a California Indian. I do because I'm on the roll of California Indians that provides me some minor benefits (established in the 1960s when the Feds recognized that they had omitted hundreds of tribes in their earlier pathetic efforts). At another scale I consider myself a member of the South Fork Hupa or Tsnungwe (this is what most anthropologists would call a tribe or subset of tribe). I am also a descendent of the Big House at Howunquet or Kentuck from the Reservation Years (when my ancestors were forced onto the Reservation). Finally, I am Hlel-we (person from Hlel-din). That's the most important village in our original territory, where my father was raised and place of my earliest recorded ancestors (it's about a mile from my family homestead). So which do I identify most with? - probably Tsnungwe. That's the group for which there is good ethnographic resources and corresponds to my extended family and family friends. In my experience, many natives of Northern California identify most at the tribal level. There was considerable traditional enmity between California tribes so I think the tribal level is perhaps more common.
For more on the Tsnungwe see Martin Baumhoff's California Athabascan Groups, 1958. Univ. of California Press, Berkeley.
Followup question, when they talked about their race as a whole what term did they use? Native, Indian, and Native american all seem to be European concepts.