Historically certainly and as a set of initials OK but the full name ignores the huge number of passengers in the North.
When the LMS was created, they considered a series of names before settling on London, Midland & Scottish.
Names in the frame were:
Midland & North Western
London, Midland & North Western
London, Midland & Northern
The Midland Railway insisted its name was included in the title.
"Scottish" was added when agreement was obtained from the Caledonian to merge into the West Coast group.
Today's operation has nothing to do with the Midland in LMS - that was for the Midland Railway which has only a tiny connection with WCP routes (at Birmingham and Carlisle, where there were joint stations).
All the WCP routes were originally LNWR or Caledonian, bar a few outliers like Wrexham, Gobowen and Shrewsbury (largely GWR) and Blackpool (LNWR and L&Y Joint).
The last mile into Edinburgh Waverley was originally North British (E&G).
Colwich-Macclesfield was North Stafford (which for a long time had an agreement with the LNWR for some of its London services to go via Stoke).
For these reasons I wouldn't go mad for a return to LM&S.
Grand Junction has as good a claim as any, as I think all WCP services touch it at some point in their journey, even after HS2, and it's the very core of the system.