It should obviously be called the Great Western Rly, TOC▸ notwithstanding.
This use of "Great" in interesting - and dates from way back in rail history?? Intertesting that "Great British Rail(way) got votes - but was a poor second to British Rail(ways)).
Olden days ... Great Eastern, Great Western, Great Northern. The exception was Great Southern which was Ireland; I suspect that competing companies were "marketing" as they grabbed territory and don't really know if that's right for the current times.
In the case of the
GWR▸ it dates back to 1833, but the epithet was applied to coach roads (such as the Great North Road) from the end of the 17th Century. It's used pretty much synonymously with 'main', rather than in the modern sense of 'much better than average', though the GWR obviously meets both criteria admirably.
The GER and GNR, like the GWR, were essentially major routes which grew into networks. Routes from London to the South-East, on the other hand, were a bit on the short side to be described as 'Great'.