I researched this name quite a bit before I gave it to my son. And all the origins I found stated that it means Illuminated Town (Day Town)/Illuminated One or David's Town. Never heard of a ditch town. I like it because it's original and unusual for a name.
The surname DAYTON is a variation of DEIGHTON, derived from the Danish, and originally meant the enclosure of the farm surrounded by the dike. The dike was usually used for the purpose of defense.