Oh please, not that old BA and the regions chestnut again - they don't care and haven't done for years. Not much different to AF (Paris) and KLM (Amsterdam) and remind me again how many other UAE cities Emirates flies from.
It's a specific business model which kind of works for them and BA are and shouldn't be no different. It's not a charity and it's not (thank god) a state airline aka a politician's play thing.
And the name - well it's what they inherited from the state sell off....there's nothing stopping a Manchester based airline calling itself UK International or England Airways.
Just need to get over it - Manchester's doing just fine without it.