From "A DICTONARY OF BRITISH SURNAMES" by P.H.Reaney, Litt.D.,Ph.D, F.S.A.; second ed with corrections and additions by R.M. Wilson, M.A. , pub. by Routledge and Kegan Paul (no date)
DEEMING, Demings: Reginald Demung 1246 SEALS (W): John Domyng 1351 AssEss. OE *demung 'judging, judgement' from OE dema 'judge'. Domyng may be an error for Demyng, otherwise from OE *domyng 'judgement', from OE dom 'doom,judgement. The surname is identical in meaning with DEEMER and DOMAN.
I had reason to believe the name to stem from Normandy or Brittany in France and THE ancestor to heve been a retainer with William the Conquerer.