The Christian name Diarmuid is anglicized Darby as well as Dermot, and similarly the surname Mac Diarmada, normally MacDermott, became MacDerby in Munster and south Leinster as early as the sixteenth century and was returned in the “census” of 1659 as one of the principal Irish names in the barony of Iffa & Offa, Co. Tipperary. As Darby it appears very frequently in eighteenth century records relating to that part of King's County (now Offaly) nearest to Co. Tipperary. In that case, however, it was an English family, the first of whom was John Darby, who, according to family tradition, came from Leicestershire with the Earl of Sussex in 1559 and took part in the siege of the O'Carroll stronghold, Leap Castle, which he subsequently acquired by marriage with an O'Carroll heiress. Judging" by the modern distribution of surnames it would appear that Gaelic Darbys also survived as Darmody in that part of the country. Two men named Derby appear frequently in the Co. Cork Justiciary Rolls of 1311 as jurors etc: judging by the other names in the same context they were of English descent.

According to Mac Giolla Domhnaigh Darby in Ulster is an anglicized form of Ó Duibhdiorma.

This is the name of a once numerous Co. Donegal sept, now known under many variants such as Dermond, Deyermott, Diarmod as well as Dermott, sometimes with the prefix O or even Mac. Ó Duibhdiorma occurs ten times in the Annals of the Four Masters between 1043 and 1454: the head of the family was chief of Breadach in Inishowen. The same name has also been anglicized as Dormer, which, however, is normally an English name (of French origin) associated with Co. Wexford, especially New Ross, since 1590. Six Dormers, of different families, appear in the Co. Wexford Inquisitions of the early seventeenth century; and of the six Dormers who suffered outlawry for their adhesion to the Jacobite cause three were of New Ross and three of Co. Kilkenny.