The name of Cushing originated in England soon after Norman Conquest of England in 1066. It was name for a person who was related to someone of note in the area. Further research showed the name was derived from the Old French, cusin, and the Old English, cousin, which means relative.
The Cushing name was first found in Norfolk and in the southern counties of England, where the first on record appears to be Roger Cusin, listed in the Pipe Rolls in that county in 1166. Robert Cusyn and his wife Joan were landowners in Ellisfield, Hampshire during the Reign of Henry III (1216-1272). Peter Cusin was a sheriff of London in 1273. A Galfridus Cusyn of Hardingham, Norfolk is mentioned in the Subsidy Rolls for that county in 1327. 
The Yorkshire Poll Tax Rolls of 1379 lists: Johannes Cosyn, tiropour; Ricardus Cosyn; and Alicia Cosyn, 1379.
Cushing Spelling Variations
Before the last few hundred years the English language had no fixed system of spelling rules and the church priests not only used latin but felt they had much more important things to do (praying) than keep records. Add to this not only missing records but damaged records and most of the people registering births and deaths being illiterate, hence the priest just guessing a spelling, and we have quite some confusion. You can add to this the issues mentioned in the First Name Varients section of this website.
For that reason, spelling variations occurred commonly in Anglo Norman surnames. Over the years, many variations of the name Cushing were recorded, including Cousin, Cousins, Cozens, Cossins, Couzins, Cossens, Cosin, Cosyns, Cousens, Couzens, Cossins, Cosin and many more.