I'm thinking of making a scenario-type map, where several European powers race to conquer and set up spheres of influence in the Americas, and to a lesser extent, Africa. But I have a pretty pressing question, I'm not sure if I should set up the colonizable areas with pre-colonial names or tribes, towns, and minor nations that existed before (genocide, probably) the colonization. Any thoughts?

i think pre-european names would be better

Its not genocide, if diseases did all the dirty work for you.

Maybe have the colonial name in parentheses after the native name.

^ I agree with this. And depending on the size of the map, Indigenous names for obscure territories might be difficult to find anyways.