Portugal has four tiers,
Alfa (basically Pendolinos, fast limited stops between principal cities only on dedicated faster tilting trains, with a price premium - so brand defined by stock, of which they only have nine and a half units)
Inter City - all other fast loco-hauled services between cities
Inter-Regional - long-distance trains but not particularly fast, but still some stops missed, maybe like UK regional rail services)
Regional - all stops, usually within one district
Both the last two categories still include some trains that do longish distances. You can’t use some tickets or rovers on the faster services, which have to be pre-booked with reservations.
I suspect this is a common arrangement in most countries.
if the UK went with this sort of set-up, you’d have the IEP and maybe Pendolino services as one tier, Inter city might pick up some cross country and east anglian services, Grand central, that sort of thing.
Inter City is still a strong brand with anyone over 50 who can remember the step change in quality and speed with the introduction of the Inter City 125 trains, and I think you’d want something with the same sort of level of stock quality to meet people’s expectation. This might exclude 2+3 seating, three sets of doors, no catering and that sort of thing. Use it to imply stock of a certain standard with fewer stops. Passengers do care about that sort of thing, it’s easier to relax and enjoy the journey and that counts for something!