But what's the real difference between having a station called London Old Oak Common and another called Manchester Davenport Green? If people have to know that the former is where they get off to go to Heathrow airport, it's not too far fetched to expect people to get off at the latter for Manchester airport.
It's fair to argue that very few people outside of Greater Manchester would have ever heard of Davenport Green, but then I'd assume that very few people outside of West London would have heard of Old Oak Common. The difference, I suspect, is that the name "Old Oak Common" was widely known in railway circles due to the GWR depo, so when it came to building the station there the name stuck.
I'm not saying that there is any conspiracy or anything, but it is interesting to contrast the differences between London, Birmingham and Manchester. All three will have two high-speed stations: a central city station and a suburban interchange for their major airport, but only the London interchange stations gets a "unique" name while the other two seem happy with "X Interchange".