Why is the District of Columbia named so?

You must keep in mind that at the time our country was founded, the states were far more independent from each other and the federal government than today. That was one of the major issues leading to the Civil War (slavery itself was in many ways a sub-issue of the states' rights controversy). The early states had markedly different demographics. The District of Columbia was not the only potential choice for our capital. The states disputed where the federal capital would be located as they were concerned any state that contained the federal capital would gain too much power. Thus, the District of Columbia was formed which is not part of any state, but rather its own "District" indirectly supervised by Congress itself.

Columbia is for Christopher Columbus, discover or marauder, depending on when you were in school.

"America" is for Amerrigo Vespucci, who received credit for discovering the New World after Spain suppressed Columbus's legitimacy.