Personally I'd go for a brand separation mainly by service type, but with regional split for the more local trains too. For example
Intercity - all long distance, high speed services, including those that weren't necessarily part of the old intercity like TPE and HS1 services.
Intercity Connect - a sub brand of intercity, for more long distance semi-fast interregional services, operated by blunt nose trains, such as Cardiff - Portsmouth, and for premier NSE services such as Waterloo - Weymouth, King's X - King's Lynn, Victoria - Brighton etc. This wouldn't be for semi-fast links where there is already a decent intercity service (e.g Cardiff - Penzance or many of the LNWR setvices) as it would be useful to be able to differentiate between service types on these routes.
Sub brands such as Scotrail Intercity where appropriate.
Overground - London inner suburban services, such as SWTs old red train network.
Thameslink - I think this brand makes sense to keep, as it is well known and it's service pattern is good to distinguish from other trains on the lines
XXXX Metro - frequent services in and close to large cities, mainly in regional rail areas, but also where possible in NSE areas (Solent Metro, Coastway Metro etc)
Network Southeast - other services in the former NSE region.
Network XXXX / TfW rail / Scotrail / other local branding - remaining regional rail services that aren't otherwise Metro or Intercity Connect
This would allow marketing of a comprehensive and impressive intercity network nationwide, but also 'local trains for local people'