Not something I thought of a lot when I was back in US since USA is… a pretty bureaucratic name by all means. But I just realized that some countries have really fascinating names in their local language
Like how China names itself Central/Middle country in a very grandiose way (as in, we are the center of the world), or Japan being “land of the rising sun”
I’m not sure what you mean by local as each indigenous nation presumably had their own way of referring to the land.
‘Turtle Island’ is the common translation for the ways that many Algonquian- and Iroquoian-speaking refer to North America.
Where I live (Lekwungen territory) means “place of the smoked herring”.