(15 Jul 2015, 9:01 pm)R852 PRG wrote You've hit the nail on the head.
...and exactly what I was getting at in my post - it would be completely illogical (and I'm afraid I still think this applies to grouping services 20 and 50 within the same brand too!)
Not sure what the point is regarding "Welcome to the land of the Prince Bishops" - these signs are at all of the Tyne and Wear / County Durham borders to symbolise how the county was once ruled (as far as I know!) Heck, if this was our reasoning for grouping these services within the same brand, we may as well chuck the rest of the County Durham services in with them too...
Not a great deal of customers will travel from terminus to terminus on either of these services - the route mainly provides local links with a couple of longer journeys from the odd customer. If customers see a purple bus, they might therefore expect to be able to travel from South Shields to Sunderland, South Shields to Houghton-le-Spring, or Durham to Rainton Bridge.
The 50 service doesn't serve any of these locations - this re-branding process you have suggested would be nothing more than completely confusing.