'operated by ........'.
:grin:
I wish the same

Unfortunately, I very much doubt BR will be recreated any time soon; even Ed Miliband hasn't commented on renationalising the railways.
You can have sections of the train that can have some branding, such as the route name (to differentiate say Capital Connect from East Anglia or whatever).
Modern stock would be better identified by those who have service specific tickets by larger displays on the front and sides to identify the service, including destination and stopping pattern etc. Maybe also include the time of the departure so people can be sure it matches their advance ticket etc.
Following on from
this thread, why not go further and give each train service a passenger reference number prefixed by category? This would at least give the passenger a rough idea of the facilities on board the train (e.g. trolley service, first class, buffet car), its average speed and how frequently it will stop.
For example, having looked at Swiss train categories, it might be able to classify all train services in the UK as follows:
EUS: Eurostar services
IC: Intercity services
IR: Interregional services - services which stop more frequently than Intercity services and run at a lower average speed.
L: Local train services
LO: London Overground services
MR: Merseyrail services
A couple of examples:
The 1821 "WAG" express from Cardiff Central to Holyhead, despite having a noticeably lower average speed than a WCML Pendolino service, would be, in my opinion, be classed as an intercity service because of the restaurant car on board. Similarly, LM services from London Euston to Crewe might be classed as interregional because they call at more stations than Virgin services on the same route.