No known historical record from the 1700's lists this John Duke with a middle name.
The Hanover Co., tax lists show this John Duke who married Sarah as just 'John Duke' residing in Hanover Co., VA from 1782 through 1798 after which his wife Sarah is listed through 1805 when she moved to Goochland Co., VA. where she is listed in the 1804 through at least the 1824 tax lists. She died before the 16 Apr 1833 in Goochland Co., See: https://www.wikitree.com/wiki/Duke-4565
Bob's Genealogy Filing Cabinet has an article on 'The Use of Middle Names' in Colonial America. It cites two genealogical studies that showed that less than 4% of Colonial Americans had a middle name prior to the American Revolution. It was with the explosion of the population after the Revolutionary War that the prevalence of middle names became the norm. See: https://genfiles.com/articles/middle-names/
Without conclusive proof that this John Duke had a middle name, he should just be listed as John Duke.