Firstly, the surname may be of Irish origin, and is an Anglicized form of the Gaelic "O'Muirgheasa", descendant of "Muirgheasa", a personal name apparently derived from the elements "muir", sea, and "geas", action, and are a branch of the "Ui Fiachra", having their territory at the southern side of Sligo Bay. These are of MacDermot stock, being descended from Muiris, the grandson of a famous MacDermot.
However, there is no Gaelic sept of Morrissey associated with Munster or Leinster. There was a very powerful family called de Marisco, whose first representatives in Ireland were Normans, attached to the house of Ormond, through which they obtained extensive grants of land. Many of the Norman families became thoroughly hibernicized, and the de Mariscos adopted the patronymic MacMuiris, and in due course this became, in many cases, Morrissey.