Can't see anything with Scotland/Scottish/Wales/Welsh in the branding which doesn't have the endorsement of the SG or WG respectively.
And they won't give that except for their own operations.
There's a whole industry around transport branding, and the tendency is to invent meaningless but "aspirational" names rather than anything geographic or historical.
Just look at SNCF's efforts (Thales, Ouigo, Lyria, Elipsos) - these are from a nationalised railway, and are all variants of TGV services.
RENFE has AVE, Avant, Alvia and Euromed (only the latter has a geographic link).
Italy has its Frecci... services, representing different levels of high speed service, none of which are geographic or historical.
Air France has Hop! and Joon brands (supposed to appeal to the jaune - young).
IAG has a new low-cost airline called LEVEL.
First's Horizon proposal was a step in this direction, c2c was another (and widely derided when launched, not so much now).
The trouble is the franchise owners' own branding are not very memorable and are likely to be ephemeral.
How long will brands like Abellio or Govia last?
On the other hand EasyJet and Ryanair didn't exist until recently, but they are now the biggest airlines in Europe.
In Australia, the NSW State Rail Authority brands its services Sydneylink (suburban) and Countrylink (long distance), both very bland.
Germany has regional names like Metronom (round Hamburg/Bremen).
Paris has Transilien (Ile de France).
Or look at cars.
Who'd have thought something called C'eed would be successful, or Mokka or Qashqai or Kadjar?
When SNCF launched the first TGV service (Paris-Lyon) its on-board service was branded "Service 270" - 270km/h (168mph) being the original speed of the new line.
It's a bit more complicated today with newer lines and trains having higher speeds (and Paris-Lyon itself has been upgraded).
Our HS2 version could have 350 in the name, if that is what the service speed will be.
IC350 would also link back to BR's IC225 (though the ECML never operated at that speed).