Irish Anglicized form of Diarmaid/Diarmait, from the Gaelic "free from envy". In Ireland Dermot or its alternative spelling Dermuit is often changed to Jeremiah although this has a different origin.
The Irish Gaelic name Diarmait [and variants] may be Anglicized as Darby although Dermot is more usual. It is for this reason that Darby may be found as a pet name for Dermot.
Derived ultimately from Demetrius [q.v.].