I'm not fond of naming train companies after the area they base themselves in. It seems wrong to me to name a service after an area when the trains are mobile, so will pass through many areas. It could also, in the customer's unknowledgable eye, suggest that the train company favours passengers travelling from a certain station. If someone regularly travels from King's Cross to Hull on Hull Trains, for example, they may wonder why it's called Hull Trains and not London Trains or Peterborough Trains even. Virgin Trains have the right idea, a neutral name that doesn't favour a particular city or region.
Another issue is with locally named companies, many passengers get similar names confused. I.e. East Midlands Trains regularly received Tweets on behalf of the former London Midland, and I would imagine similar mistakes are made with Southern/South Eastern.
I notice the OP mentioned Midland Mainline, well that name made sense, given that the majority of stations served were on the Midland Main Line. Even if that branding wasn't trademarked, it would be wrong to reinstate that name, as the franchise now also operates services from Peterborough-Doncaster, not even touching the Midland Mainline!