The form of the name "County Durham" is unique in England. Many of the counties named are named after its county town for example Yorkshire and Warwickshire.  However Durham did not become  Durhamshire it is County Durham and the naming is related to the former sphere of influence  the bishops of Durham wanted the inner areas to be distinguise from the outer areas.

History of Durham
In Roman times, a strategically important road went right through the county.  Its purpose was to defend the northern border of the Roman Empire.Even today, remnants can be seen from this period, as a Roman fortress at Bishop Auckland.
Already by the death of the Holy Saint Cuthbert won the County Durham in religious significance and became a pilgrimage site.  But as William the Conqueror in 1072 winning bids for the bishops of Durham special religious and military power, it gained a status that allowed them to include the construction of the magnificent Norman cathedral.  Together with Durham Castle, which was the seat of the Prince Bishops until 1832, it still reflects the power and wealth of the bishops resist.
But not only the bishops but also many wealthy and influential families demonstrated their position through the construction of palaces and other magnificent buildings.  With the advent of the coal industry in the 19th  Century, many managed to increase their wealth.
Variety of landscapes makes the county of Durham today particularly attractive: From the coast to the east, over moorland and one of the largest forested areas in northern England to the North Pennines in the west - the County Durham has something to offer for every taste.
More information
Cities in Durham : Durham , Darlington