Jim was the last child that David and Lucinda had until several years following David Hunt's return at the end of the Civil War. Jim likely didn't remember his father as did most (or all) of their other children.
Jim altered his name a number of times and also had multiple marriages with children from each. In later years, Jim made his middle name his first name and added an initial, H. Thomas H Hunt is Jim Thomas Hunt.
Marriage certificates from Nippers, Marville and Tidwell
It may be possible to confirm family relationships with Jim by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: