Personally would argue that the British Railways brand is not as toxic as some people here seem to think - its 2020 not 1985. People have moved on and forgotten. The whole advertising and marketing world has changed beyond recognition. Its a clear and consistent message. People would know what it is. Besides, heritage brands seem to be enjoying a resurgence - GWR, LNER, LNWR... - and compared to some of the 'modern' innovations - GTR, Southern Fail, Northern - have a better public image.
I'd suggest that the end of the franchise system will probably result in an umbrella central organisation - BR - and within that some sort of sectorisation along current franchise lines and hunkering after nostalgia they'd stick with the familiar... Great Western Railway, LNER, Midland Railway, London and North Western, South Eastern Railway, ScotRail (maybe Caledonian).
I can't think of anything more dull than branding something 'Regional Railways'.
Then again, if thinks become a tiered system - local and intercity services - then I wouldn't be surprised if some sort of generic Intercity brand is created for West and East Coast, Cross Country and GWML services. HS1 becoming SE Javelin. And then a return to the more regionalised franchises of the early 2000s - Wessex Trains etc.