You also hear quite a few people refer to the Great Northern services as "Thameslink" -although to be fair a lot of Thameslink branded stock got used before the St Pancras services started.
Are some Great Northern KGX services still operated using "Thameslink" branded 700s if these are not 365s?
It seems some people can't help referring to something by its previous name than the current. The power of marketing or longevity of the brand is the key - Virgin Trains is a powerful brand more recognisable than Avanti West Coast also SWT ran for so long to be remembered more than SWR.
AWC has rather large shoes to fill as VT's replacement, it's quite clear that First Trenitalia chose a modern trendy name with Italian flair, for their West Coast franchise, trying to capture Virgin's cool appeal but obviously not as good. As at the time just before AWC first debuted, it was widely predicted that First Trenitalia was going to use LMS with the Avanti name reserved for the new HS2 trains because traditional names ending with Railway were being adopted by new TOCs.
LMS as a brand, in retro style like EMR or GWR, probably wouldn't have the same appeal as VT & AWC if the customer has modern tastes and is social media obsessed.
LNER, in a way, seems to work as a brand for me as it is a more modern style than retro which I think helped by the new Azumas also continuing the bold red scheme left by VTEC. If LNER started off on a different path like going with a very old fashioned looking brand and dark blue scheme then it may be harder for it to retain the strength of the Virgin brand it would be taking over from.