*The Highland Chieftain. The Highland Sleeper (Inverness portion) doesn't count, as boarding at Edinburgh isn't valid
The Highland Chieftain is not a sleeper service, it is the Day service from Inverness to London Kings Cross operated by East Coast. But it's ok many local and national politicians make the same mistake.
As far as I'm aware, there is no names for the Sleeper services in Scotland, It used to be the Royal Highlander for Inverness, Deerstalker to Fort William, Granite City to Aberdeen and Night Caledonian for Glasgow, can't remember Edinburgh's portion. But that was back in Intercity days. As confusing it must have been at Euston to have 1 train called 3 different names, I think it was an important part of the campaign to save the Deerstalker, because it had a recognisable name to all the locals who used it, and other's who were familier with the area.
Back to subject, BritRail pass holders (non-uk all lines ticket) get priority to first class sections to trains north of Inverness. But the standard of First Class is shocking, maybe it's because Scottish (I am Scottish by the way, but I still travel first class if it is proper 1st class) people don't like to see anybody above there station and everybody should be treated the same. Or it could just be that the small amount of people who would actually use it, the revenue would not cover the cost of improving facilities, making them larger and losing more Std Class seats which are already at a premium.
Going forward, I can see longer trains in Scotland, which if space permits, a larger first class section will become more popular across the fleet, encouraging more people to use it. But I would rather see catering improved on Scottish Services, especially between Inverness/Aberdeen to the Central Belt, as many of the busiest services run through meal times, and Scotrail are missing a trick here.