The McMURRAN name appears to originate in Ireland although it is also found in Scotland and to a lesser extent in England.  McMORRANs from Scotland have migrated to Ireland over the centuries at least as far back as the time of the invasion by Cromwell's armies.  There are also some Irish families bearing the surnames McMORRAN (and McMORAN) derived from the surname MORAN that have no Scottish antecedents.  No doubt the surnames of some of these Scottish and Irish McMORRAN have been mispelt as McMURRAN over time and this misspelling has been perpetuated.  Other variations of the surname spelling found in Ireland include McMURREN and McMURRIN. The McMURRAN surname became increasingly common in Scotland during the 19th century especially in the south-west due to the wave of Irish immigrants who settled in Scotland between 1820 and 1900.  Over half of the McMURRAN adults listed in the 1881 census of Scotland for instance are of Irish birth. 

The nineteenth century saw many Scottish and Irish families emigrate to distant shores.  The main destinations for McMURRAN families were the USA, then Canada, Australia and New Zealand.   One American family who spell their surname both McMURRIAN and McMURRAIN appear to have originally spelt it McMURRIN.  Most of the McMURRANs in America and Canada are of Irish descent.