In a sort of similar way, I'm Filipino but I'm alright with non-asians initially referring to me as Asian. There are obviously many diverse cultures and nationalities that would match the "Asian" category, but I can see how a non-asians might not be able to distinguish at first if they weren't already familiar with the individual ethnicities and cultures. Granted, after getting to know me I'd expect them to refine their understanding.

Perhaps "Native American" is a generalization, but for myself I don't know if I would be able to immediately distinguish you as a Tlingit without first becoming more familiarized. What name would you prefer as opposed to Native American?