One could argue that rebranding MME was too costly, but if MME wants to receive traffic from people who reside outside the UK, it needs to be named after a geographical location that is well known.
Most non-Italians who see an advertisment for a cheap flight to 'Orio al Serio' will have no idea where it is and ignore the advertisement. Change the name to Milan-Bergamo and people start to take notice
In my humble opinion, EMA should be named after Nottingham or maybe Leicester. 'East Midlands' is a bland PC name that conveys little or nothing to people not living in or from the UK. It's almost a way of saying 'this is an airport only for English residents'
Durham may not accurately reflect the airport's location, but both name recognition and the city's inclusion in travel guidebooks do at least help market the airport to visitors. The money on rebranding has already been spent - MME needs to make use of the assets it currently has.