Of course colonists committed genocide against indigenous people everywhere they went. No one's denying that. I'm addressing precisely what you yourself said
> there were multiple indigenous political entities both along the Eastern Seaboard
They were fragmented and smaller than the Aztec empire. That doesn't make it right to take their land. It does explain why their names didn't apply to the entire land. Because none of them was so big and centralized. If you look at the geographical features of the Eastern seaboard - mountains, lakes, streams, rivers, cities and towns, even 2 states (Massachusetts, Connecticut) - native names abound.
The lands that became the US and Canada really did have fewer people living on them than the lands that became Mexico. [1] Again because Mexico had centralized states and large-scale agriculture capable of supporting large populations.
https://en.wikipedia.org/wiki/Population_history_of_the_Indi...
