The origin of the Fitzmaurice surname comes from two main sources, both of which date back to the Norman Conquests.  The first group comes from descendants of Walter FitzOtho.  The second group are the descendants of Maurice de Prendergast.  It should be pointed out that during this time the patronymic naming system was used.  How this worked is that a person's last name consisted of the word "fitz" and their father's first name. A name such as John FitzThomas would mean John, son of Thomas. John's children would in turn use the last name FitzJohn.  The word fitz comes from the same origin as the current french word for son, fils. 

Barons of Kerry

Walter FitzOtho is known from the domesday book.  This is the oldest documented taxation of land in England, which occured in 1086, following the Norman Conquest of England in 1066. FitzOtho's grandson, Maurice FitzGerald was a participant in the 1169 Anglo-Norman conquest of Ireland. As a result of Maurice's service, at least five of his sons held land in Ireland. Maurice FitzGerald's grandson Thomas FitzRobert was the first to hold land in County Kerry, founding a Franciscan Abbey in Ardfert in 1253.  Thomas' son Maurice FitzThomas was made 1st Baron of Kerry and Lixnaw in about 1295. The 6^th Baron of Kerry and Lixnaw, Patrick FitzMaurice d. 1410 was the last to use patronymic naming.  His successor was his son who was named Thomas Fitzmaurice, not Thomas FitzPatrick.  All future descendants now carried the name FitzMaurice. Patrick FitzMaurice, the 17th Baron, was the last to be born in Ireland . All subsequent Barons, and eventually Earls of Kerry, were born and lived in England . Therefore, all Irish Fitzmaurices descending from this group trace their ancestry to at least one of the Barons of Kerry who lived before Patrick, the 17th Baron's lifetime, the 1600's back to the 1200's.  

descendants of Sir Maurice dePrendergast

Maurice de Prendergast was a Cambro-Norman knight who accompanied Strongbow, Earl of Pembroke to Ireland in 1169, participating in the Anglo-Norman conquest.  He lived from 1145 to 1205 and died in Kilmainham, near Dublin.  He had two sons, Philip and Gerald.  His younger son, Gerald de Prendergast was the founder of the Prendergast descendants in County Mayo.  It was his descendants who took the name FitzMaurice.  In this case, Fitzmaurice,son of Maurice, can be said to refer to sons, or descendants of Maurice de Prendergast.  [thepeerage.com Burke's Peerage,Baronetage & Knightage, 107th edition, 3 volumes., Charles Mosley, editor,Wilmington, Delaware, U.S.A.: Burke's Peerage (Genealogical Books) Ltd, 2003,volume 2, page 1603].