I have info that says the name was originally "Delahaye" or "De La Haye". The info says that the family were originally French farmers who moved to the Channel Islands to avoid religious persecution. They first came to Maryland and settled in and around Talbot County in the late 1600's-early 1700's, I understand.
My line goes back through Arthur G. and Sally Brooks Dillehay in Person County, NC. Their son William David is my great-grandfather. I have a fair amount of info on my full line. I would be willing to share what I have.