Of course this may have nothing at all to do with your personal name, but based on my own genealogical dabbling, the surname Demaree is at least sometimes found identified with the French surname Demarest. That might help you, a teensy bit. Or not. Good luck.
I found the following at ancestry.com http://www.ancestry.com/facts/Demaree-family-history.ashx
Demaree - Americanized spelling of French Desmarais.
Demarest - French: regional variant of Desmarais.
Desmarais - French: habitational name for someone from any of various places named with Old French mareis, maresc ‘marsh’, as for example Les Marets, in Seine-et-Marne, Centre, Nord, and Picardy.