I was wondering what the word Deerness means today.
In Scotland there's another Deerness, it's a parish in Orkney and it's an Old Norse word " Dyrnes" meaning "the state or quality of being a deer".
This is pretty cool as deer are fun animals and do roam the valley here. They seem super resilient, in that they can exist in places as hard as the arctic circle, and they eat quite a wide range of things in their herbivore diet including lichen which doesn't even resemble food!
Another site talks about our river specifically and says
"Further south, a smaller County Durham river, the Deerness combines the Welsh element ‘dwfr’ meaning river with an Indo-European element ‘nesta’ meaning , ‘roar, rush’ that is found in names such as Loch Ness and Inverness."
Which would mean that the River Deerness would be rushing roaring river.