During his (very brief) time in Congress, Horace Greeley submitted a bill renaming the country to "Columbia". Good thing it didn't pass 
Such a proposal would naturally be a non-starter, but I've always found the country being named "America" as a bit generic and bland, while all other American countries (even big ones like Canada and Brazil) have unique names. It is sort of an odd situation in that, to my knowledge, the only collective name for the colonies that would have existed was "America", which just so happened to also be the name for the region as a whole. In some sense, it's sort of appropriate in that you had a collection of different colonies come together as "The United States of America". The unique names would have emerged in an alternate timeline where each colony or region of colonies chose its own path ("Virginia", "South Carolina" "New England"...). If my basic memory of history is correct, the reason that each country in South America has its own name is that projects for a "United States of South America" fell through in the early nineteenth century. FTR, "Columbia" would have been a profoundly ahistoric name for the country.
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