Probably ‘farmstead of the children, i.e. one held jointly by a number of heirs’ from OScand.
barn +
bý; alternatively ‘farmstead of a man called Barni or Bjarni’ from OScand. pers. name +
bý:
Barmby Moor East Riding of City & County of Yorkshire
Barnebi (1086) (DB),
Barneby in the More (1371). Affix is OE
mōr ‘moor’.
Barmby on the Marsh E. R. City & County of Yorks
Bærnabi (
c.1050),
Barnebi (1086) (DB). Affix is OE
mersc ‘marsh’.