Could they have used LNWR officially or is that either protected by historic means or protected by Network Rail who I believe use the term London North Western Route to define the WCML?
The LNWR name (lnwr.com) was purloined by the maintenance company at Crewe owned by Pete Waterman.
Arriva then bought the operation and renamed it as Arriva Traincare, but I think they still own the rights to the LNWR name and web site (it redirects to arrivatc.com).
Ultimately, the DfT owned the rights to the old railway company names, as a result of buying out the Big 4.
Clearly names/brands like GWR and LNER have been reused by modern TOCs, but what the licensing terms are I wouldn't know.
NR's LNW Route isn't a company or brand (although it might well become one in the Route devolution process), so there's no commercial conflict.
The same with the LNE Route and the LNER TOC.
We'll have to see what the WCP franchise will be called when HS2 operation starts.
If we are being picky, VT/WCP has at least as much claim to the LNWR name as WMT does, which only operates over the southern half of the old LNWR route.