The families with a "Fitz-" prefix go back to some of the supporters and soldiers of William the Conqueror, the first Norman king of England.  It is an Anglican adulteration of the French phrase of "fils de" meaning "son of". This is typical naming technique found in Scandinavia and Scandinavian settlements such as in Scotland or Ireland where "Mac" is used.  This prefix identifies the family with associations to early Scandinavian invaders and settlements of Normandy, France and England. Normandy was the home of Viking families and supporters of the Edward the Confessor, Harold and William the Conqueror. 

William's invasion of 1066 established the unification of England.  The invaders were given land as a prize which was maintained from that period to the present.  Earliest connections go back to some of the first Danish kings,  Gorm the Old of about 936 was succeeded by his son, Harald Bluetooth. Harald went off each season for raiding and pillaging from Denmark to Normandy.[wikipedia.org]

Robert Fitzharding, through the positions of his father under King Edward the Confessor, became a burgess in Bristol and owner as the 1st Earl of Gloucester to extensive estates including Redcliffe, Bedminster, Liegh, Portbury and Billeswick. He had been a supporter of Henry Plantagenet, Duke of Aquitaine, the rival of King Stephen (1135-1154). The Plantagenets dispossessed Robert of most of his holdings because he wouldn't swear alligiance to them.  King Stephen eventually become Henry II (1154-1189) and restored the property to Robert and made Berkeley among his rather vast holdings the center of the new barony.  He was now the Roger de Berkeley and received a charter to build a castle at Berkeley.  Roger make several endowments to the cathedral at Bristol and his wife, Eva, becomes the abbess of the Augustinian nunnery of St Mary Magdalen on St. Michael's Hill, Bristol. [wikipedia.org]