Who do villagers believe the headless horseman is?

Answer 1

The legend of the Headless Horseman begins in Sleepy Hollow, New York. The Horseman was a Hessian of unknown rank; one of many such hired to suppress the American Revolutionary War. During the war, the Horseman was one of 51 Hessians killed in a battle for Chatterton Hill, wherein his head was severed by an American cannonball. He was buried in a graveyard outside a church. Thereafter he appears as a ghost, who presents to nightly travelers an actual danger (rather than the largely harmless fright produced by the majority of ghosts), presumably of decapitation.

In other words, they don't really know his actual name.