District of Columbia is called so because it means to refer the city of Washington as the capital of the USA. On 16th of July 1790, the Residence Act is signed to approve that an area, named in honor of the President George Washington, to be the permanent capital for the government of the United States. The Constitution established the site to be a federal district, meaning it is not a State, thus the Congress has complete legislative control over the local government. This ability is called “District of Columbia home rule”. The idea of a federal district is usually meant to be the example to the 50 States of what a government should be by having the Congress to be the government itself. In other words, they are almost entirely governed by the Congress, with the people originally barred from even voting for the President of the United States until 1964.
Anyway, why is it called District of Columbia? We need to look back at the history first. Initially, the federal district is named the city of Washington, while the city surrounding it was named the Territory of Columbia (after the founder of modern USA, Christopher Columbus). In 1871, Congress decided that the city and territory should be one, now being called the District of Columbia. In a real ironic fashion, the city that is named after the father of Democracy ends up having no power over its own local government decision, with no voting rights and representation. In another tragic fashion, the district is true to its Columbus way, of colonialism, the invasive and tyrannical rule of the natives and their own people at the time. There you have it, the District of Columbia, called so since it is the capital and appointed as the federal district of the USA.