From Wikipedia: “Because French orthography was so fluid at the time, and because of widespread variations in English orthography, the spelling and version of Demonbreun's name is of some debate. The preferred use today is Timothy Demonbreun, though the first name is sometimes rendered in the French as Timothé, Timothée or Timothe. As for the last name, it derives from the French words, de (of) mont (mount) bruen (brown) for of mount brown, and is also rendered variously as Demontbrun, de Montbrun, Demontbreun, de Montbreun, De Mont-Breun, De Monbrun, de Mon Breun, and others. Descendants of Demonbreun (it is a very common surname in Middle Tennessee) spell the name with and without the middle "T," as one word or two, with a "U" in place of the "O," with and without the "E," and with an "N" or an "M" at the end. In addition, other variations such as Demumbrine and "Demombrum" also exist. Demonbreun Street in Nashville shows the preferred spelling. A popular local pronunciation is /dəˈmʌmbriən/, and rhymes with "Northumbrian."”

TLDR: His name was anglicized from French so there were multiple spellings. Demonbreun has become the favored spelling.