What's in a place name?

I should warn you that there's a hidden counter on this blog that tells me, among other things, which country each visitor comes from.

Recently, quite a few have come from India, from where some, according to data from India, come from a place called 'Bombay', not from 'Mumbai', as the BBC and other news programmes have been calling it all this week. 

I find this very reassuring, as the British media has taken to telling us that there is something politically incorrect about calling cities by the names we've always known them by -- or, to be more precise, cities that are a long way away from Europe.

So this year's Olympic Games were not held in Peking but in 'Beijing' (though we have yet to be notified as to whether we're now supposed to call Pekingese dogs 'Beijingese' dogs).

But there are plenty of cities in Europe that are called something different by people from other countries in Europe. I've never heard any Brits complaining about the fact that the French say 'Londres' when we call it London.

And do Austrians complain when we call their capital city 'Vienna' rather than Wien, do the Czechs complain when we call theirs 'Prague' rather than Praha or the Italians when we talk about 'Rome', 'Florence', and 'Venice' instead of Roma, Firenze and Venezia?

We also say 'Moscow' when the Russians say 'Moscva', 'Gothenberg' when the Swedes say 'Göteborg' (and pronounce it 'Yerterborrier') and 'Copenhagen' when the Danes say 'Kobenhavn'.

None of this seems to cause anyone any problem at all, and even the media have so far made no attempts to correct the way we all refer to these cities. 

So, if the Indians themselves are quite relaxed about referring to Mumbai as 'Bombay', why on earth do our broadcasters and newspapers keep telling us to call it 'Mumbai'?