The Irish surname Conaway is commonly found as MacConaway and is a variant of MacConway, particular to County Donegal in the very north of Ireland, although curiously the surname is not native to the county. The form Conaway is also found in Sligo and Leitrim. The surname is used as the anglicized form of two Gaelic names, Mac Conmheadha and Mac Connmhaigh, both of which were powerful septs of Thomond until the end of the fourteenth century. The Mac Conmheadha sept derived their name from the Gaelic Mac Cu-Meadha, meaning "son of the Hound of Meath", and claim descent from the Chiefs of Muinnhear Laodhachain in Westmeath, a sept long dispersed throughout Ireland. The Mac Connmhaigh sept find the root of their surname in the ancient forename Connmhach, thus in this case the surname implies "son of Connmhach". Woulffe suggests that the Mac Connmhaigh sept are synonymous with the O Connmhaigh of Thomond, a Dalcassian family who were ollaves (chief  "professors") of music, although by the end of the sixteenth century the O Connmaih sept had largely dispersed in the south. Both the Mac Conmheada and the Mac Connmhaigh fought under the O Briens in 1317, while in 1360 is recorded the death of on Gillananaev Mac Connmhaigh. Another occasional source of the surname Conway or Conaway is the Gaelic name O Conbhuidhe, "descendent of Cu-buidhe" ("yellow hound"), although generally the surname was anglicized to Conboy or Conaboy. The surname Conaway may occasionally be derived from the Welsh name Conway or Conwy, signifying one who dwelt at Conwy. In 1340 in the Registers of the Coventry we note one David Coneway.

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