The county is referred to as the `` county of Durham '' in the amendment to Order 2009 of The Local Government legislation for miscellaneous amendments and other provisions regarding structural changes .
However , a later amendment to that legislation , refers to the `` county of Durham '' ; the amendment allows for the unitary council to name itself `` The Durham Council '' , however the council has retained the name of Durham County Council — with either option , the name does not include County Durham .