There are a variety of spellings:  Cooper, Couper, Coupar and Cowpar.
Originally it was an occupational name  of 'couper' a maker or repairer of barrels but may also be topographical from the area of the town in Fife.

The earliest of that territorially connected name was Salomone de Cupir who witnessed a charter in 1245. Simon Couper swore allegiance to Edward I in 1296. There is no general clan for the Coopers so care must be taken on adopting badges and mottos etc.  The tartan is used by all with the name.  

Its origins are not clear but was in existence in the nineteenth century.