the (oak-)wood of the awkward, left-handed people
ciotach — probably a sobriquet in this case

Doire na gCiotach most likely means ‘(oak-)wood, grove, thicket of the awkward, clumsy, left-handed ones’. However, one should probably not think of na gCiotach ‘of the awkard, clumsy, left-handed ones’ as a reference to a random collection of such people, as it most likely refers to the sobriquet (nickname) of a particular family who once had possession of land here. Ciotach was quite commonly used as a descriptor in Irish society, and sometimes seems to have been applied to families inter-generationally. For example, a reference to ‘Hugh Kittagh Mc Owen Kittagh, of Inche’ (1605; Calendar of Patent Rolls (CPR) 65b) i.e. Aodh Ciotach mac Eoghain Ciotaigh [Ó Murchú] of Inch [#52315], near Blackwater, in County Wexford, suggests that this branch of the Ó Murchú family bore the sobriquet ciotach, as it has clearly been passed on inter-generationally here. Indeed, in the same entry to the CPR one also finds ‘Edm. Kittagh of Inche’ (Éamann Ciotach), probably another member of the same family. Such a scenario allows for Doire na gCiotach to be understood as a reference to the sobriquet of members of a particularly family, most likely erstwhile landholders here.
(Conchubhar Ó Crualaoich, An Brainse Logainmneacha)