Dillard is indeed originally a surname. It is quite common in parts of the state of Virginia
. Unfortunately the only dictionary I have in my office that includes it is _The Encyclopedia of American Family Names_ by Robb and Chesler. That one is not the most reliable source for etymology; it claims it is a variation of the surname Dill, and Reaney & Wilson
's _A Dictionary of English Surnames_ says that the origin of Dill as a surname is difficult to figure out; if may go back to an Old English given name, Dylla; it could be from a nickname, Dull (meaning unfortunately about the same thing that it would today); or it could be for someone who sold the spice Dill. But I think we need more evidence before assuming Dillard is really connected with Dill.