The name “Purim,” in fact, reflects one of the core lessons of the holiday. A raffle or lottery, such as the one Haman cast, is an arbitrary choice, one disconnected from any system of logic or preference. Haman deliberately avoided rationalizing a certain date as propitious for destroying the Jewish people; his selection of the date was entirely random, specifically because Haman wanted to make spiritual use of the essence of a lottery. He reasoned that just as casting lots is a non-preferential choice, so too, there must be a spiritual plane where G-d, due to His exalted nature, does not have any preference for the Jewish nation over any other, and therefore, He would not protect them from destruction. Haman was sure he had the system all figured out, but...

...he was way wrong. While there does exist a level at which variations cease to exist, where even opposites do not clash (light and dark are the same; good and evil are irrelevant)—even at this supra-spiritual plane—G-d chooses the Jewish people. There are times when G-d’s apparent relationship to His people reflects our spiritual standing, hopefully for the better. However, G-d’s essential affinity for the Jewish nation is not based upon our worthiness at all. We are forever G-d’s children, come what may, and G-d will never allow our enemies to prevail over us.

Thus the name “Purim” appropriately represents the meaning of the holiday, G-d’s immutable choice of the Jewish people. Therein lay Haman's miscalculation, and he really got himself into 'a lot' of trouble.