Hi there,

There's definitely more room for discussion, but you might be interested in this answer of mine to a very similar question. It deals with names of the Aztecs (in modern day central Mexico) and Incas (in the Andes) for their known worlds, in pre-colonial times.

Please note as I mention there that there was no idea of "one" native Americans, rather there are until today many hugely diverse groups with different notions of their lands - the simplifying term of "Indians" or indios to describe all these groups was first introduced by Europeans during colonisation.

Hope this helps and that others can add, esp. also for the modern-day US.