Although I generally loathe the idea of branding, I suppose something like the 'Tynedale Express' or the 'Hexham Clipper' might work for the X84.
I don't see how the Derwent theme would be an obvious suggestion. The closest the current route comes to passing the Derwent is going along the West Road into Newcastle. However, if the X84 was ever to be extended beyond Hexham and onto Carlisle, the old 'Cross-Country' branding could be borrowed from Derwent and applied to the service.
RE: Go North East