Does the LNER example that started in the 1920s (ie having both a loco and a service with this name, but not always using one on the other) "not sit comfortably" either? This is after all the "heritage" that EC are invoking
Well I was not around in those days for it to bother me.

However back then, there were locomotives that were named, and titled trains that had headboards, so there was a distinction.
Today headboards are not generally used, and this locomotive is not named, it is purely an advertising livery, emblazoned all over the locomotive, not a more subtle name plaque.
Also as to comment on Darlorich's point. I am not saving that 91101 should be used exclusively on the Flying Scotsman, I am just saying it does not seem right to see it on other routes implying to the general public that this is the Flying Scotsman. Maybe the branding should be changed to something like. 'East Coast Railways Home Of The Flying Scotsman', or something similar.