The popularity of and reverence for Christopher Columbus in the United States is more than a little puzzling. That an Italian mariner of bewilderingly little talent, sailing for the Spanish crown, who landed in the Bahamas, Cuba, and Hispanola (today's Haiti / D.R.) became an American icon makes sense only in the context of American culture and society immediately after independence from Great Britain.
As new nations always do, the US experienced a fit of nationalism and a backlash against all things reminiscent of the now-hated British. For the first two centuries on the North American continent, we had played the role of loyal subjects to the Crown and accordingly most pre-Revolutionary places and institutions bear distinctly British (or less commonly other European nations') overtones. We have states, for example, named after William Penn, Queen Elizabeth (The Virgin Queen, hence Virginia), the British Channel Island of Jersey, King George II, the Duke of York, and the 3rd Baron De La Warr, not to mention two Carolinas named after Charles I and countless cities named after the likes of Lord Baltimore. Very suddenly in 1776 it became highly unfashionable, bordering on socially unacceptable, to show pride in any name that served as a reminder of the humiliating subjugation to a faraway island in Europe, and henceforth only good American names would suffice.
The problem was that America didn't really have any American history distinct from that of Britain upon which it could draw. There were the Native Americans – and indeed many Native American place names dot the map east of Ohio – and some admiration for the French who had aided us during the Revolution (Lafayette and King Louis both became popular naming inspirations). There were also living American icons, primarily Washington, but one could only name so many things after a man who was still living and around whom many feared the development of a cult of personality. So that is how Americans at the time seized upon an Italian mariner of bewilderingly little talent, sailing for the Spanish crown, as a national icon. Columbus, who had very rightly been completely ignored and forgotten in this country up to the American Revolution, suddenly became America's founding saint for the sole reason that he was untainted by any association with England.
First there was the transmutation and anglicizing of his Spanish name, Cristobal Colon, to something he was never actually called during his lifetime (the British also did this to Giovanni Caboto, "John Cabot"). Then the fact that he did not land in any part of what was actually the United States was swept under the rug, deeming it sufficient that he had landed in "The Americas." Finally, that Columbus was a poor mariner who insisted to his death that he had landed in Asia was deemed historically irrelevant. And then we started naming things after him with a vengeance.
From 1776 until about 1800, nearly everything of consequence requiring a name in the new United States was dedicated to Columbus. The classically British-sounding King's College in New York became Columbia University (1784). The region of the American Northwest explored beginning in 1793 was called Columbia (which lives on today in the part that was retained by Britain after a treaty: British Columbia). The Ohio Territory had its future capital, Columbus, established in 1797. South Carolina renamed its capital Columbia in 1786. The District of Columbia was chosen as the site of the future national capital (1790) with the Residence Act. A march written for George Washington's inauguration in 1789 became "Hail Columbia", America's national anthem until it was replaced with the Star-Spangled Banner in 1931. Counties, towns, bodies of water, and other geographic features almost too numerous to count were similarly given some version of Senor Colon's non-name as were scores of Columbian societies and institutions, one of which eventually became the Smithsonian Institute (that story will have to wait for another day).
Half of success in life is showing up. And that's how Columbus became indelibly stamped into the fabric of the United States: by not being British at a time in which lots of new things needed names.