That was the rather long and uninformative headline a few days ago in the local newspaper. They couldn't say "Terrorists Strike in Mumbai" because few of the local rag's readers know in what country "Mumbai" is. Readers have heard of "Bombay." They've eaten at Bombay Bicycle Club restaurants and they've bought end tables from Bombay Co. Furniture stores, so they mostly know Bombay is a city in India. But, Mumbai they don't know from Kolkata or Chennai. So, the headline writer has to refer to "Indian City" because the English-language media recently stopped using the place name that has been used in English for centuries.
The effect, of course, is what normally happens when names are changed. The Name Game just makes most people more ignorant (while giving a few people another reason to self-congratulate over their superior sensitivity). Older Americans who grew up hearing about Bombay can't understand today's news; and younger Americans who are growing up hearing about Mumbai won't be able to understand all the books in the library that refer to Bombay.