There is definitely one apparently new market in the post Covid economy that would benefit greatly from branding as a means to alert potential customers to the benefits of the railway: the staycationers (not sure if that is the correct term, but to avoid doubt I mean holiday makers who stay within the UK).
If you assume most resorts, holiday parks and tourist towns are best arrived at just after lunch to facilitate the usual budget hotel check in time, then you could identify and market all direct services to these places under a single national brand.
The [Placename] Staycationer is perhaps a little lame, but you definitely want something new, relevant, and you certainly want to avoid clichéd and potentially inaccurate terms like Express or Special. The services are unlikely to be expresses, and are unlikely to be special in the loading sense.
You'd have to limit it to specific smaller and thus potentially less well known destinations, on the assumption most people know that places like Edinburgh are accessible by rail from a wide range of destinations (the dirty secret of the railway of course being how limited your options really are if you absolutely need to be in Edinburgh by 2pm and don't live in a convenient place).
Hopefully most services could take advantage of spare capacity of off peak travel, but those tiny few that don't, could as a rule have a certain amount of seats reserved as if they were off peak products.
I guarantee most people, even regular railway users, have absolutely no clue what the rail options are to get to a place like Windsor or Whitby for 2pm. And without knowing it, they may never consider going there.
You could even subdivide the brand by categorising each destination - coastal resort, holiday park, amusement park, heritage town, or general tourist destination.
You could produce promotional maps of all Staycationer services, run marketing campaigns and offer discounted tickets to people holding hotel bookings or resort passes.
Obviously you would also highlight the most useful services (timing, route, ease of transfer, facilities at transfer) that could connect with your branded trains, without cluttering the brand and confusing the customer by telling people about the whole railway network.
Where possible, you ensure these branded services have ample luggage space and a fully stocked lunch trolley, perhaps with a complimentary tea and biscuit to the passengers who have the discounted tickets.
You do the small things that make customers feel special, valued, like you actually do care that they chose you over the far more convenient option, the car.
And you obviously always make sure there are train and platform staff to check tickets and field questions for these specific services.
You don't bother putting the brand in timetables or on departure boards but you do otherwise make sure visitors to specific stations looking to catch these services are made well aware through AV means how and where to catch the branded train.
You obviously seek to partner with the organizations you hope to be bringing extra custom, at a minimum seeking their help in brand awareness, without becoming distracted and forgetting the main aim of the brand is to get bums on seats.
Partnering with taxi firms for the last mile is also obviously an option, but not something you would start out with until you were sure of demand.
Maybe you even find some D-List celebrity to front the brand. Someone recognizable but hard up enough to not complain about being sent around the country to smile on local TV news as they talk up the benefits of the Staycationer as an affordable, relaxing, enjoyable and of course climate friendly way to start your domestic holiday.
You set minimum standards in how the brand is to be presented and the services provided, and fire anyone who treats this like a hassle or an optional extra to their day job. You use secret shoppers to ensure the brand is meeting expectations.
If the railway really got its act together, I'm sure it could apply prominent vinyls to the specific units allocated to these diagrams, which would identify to the public which departures and which destinations of that particular train fall under this national branding effort.
