What is the name of the headless horseman's horse?

DAREDEVIL IS NOT the horse's name. If you read the book you'll see that the horseman's horse is never named.

Daredevil was the name of the horse of Brom Bone. In the story Brom Bone boasts that he and Daredevil raced the horsemen one night. At the end of the book it is never made clear in the book that the HH was Brom Bone or not.

That being said, you can't claim that the Horsemen's horse is Daredevil because their is no solid proof of it.

It is commonly believed that the horse was named Daredevil. For example: in the movie by Tim Burton the horsemen's horse was called Daredevil. But if you are one of the few people smart enough to read the original story by Washington Irving you'll know that the horse has no name.