Take it from someone who lives and works overseas there is no better name for the airport than Manchester. Thanks to the city's long history and even more famous football teams it's a name that is instantly recognized world wide and for all the right reasons (except perhaps the weather !)
In Australia they even still refer to their bed sheets and other household linen as "manchester" !! On the other hand names like East Midlands or Humberside would have many overseas travellers reaching for their Google maps.
If there was a good reason to change the name to Manchester Ringway I don't think I'd object, but Manchester has to be in there