The District of Columbia has nothing to do with the country of Colombia. They both got their names because Columbia is another name for America.
When the Founding Fathers created the US political system, they were aware that if the capital of the country also has representation in the legislatures, it will have disproportionate influence on laws and government policies. (You can look at capitals like Prague, Moscow and Paris to see how they suck in a disproportionate amount of their countries’ resources and receive most of the benefits.) They therefore wanted the capital of the country not to be in a state, and not to have legislative representation. Therefore, they created the District of Columbia as a neutral zone that does not have representatives or senators in Congress.