While watching a Bollywood movie "Wake Up Sid" there was an interesting disclaimer about how there were references to Bombay instead of Mumbai. So I switched tabs and read up a little on history.
In 1990's, while I was half paying attention to the news in the world, a group of people changed the names of several cities in India to be more in line with taking off the shackles of colonialism and other factors going on in their slice of the world at the time.
It makes sense now from what I've been reading, watching, and even the airport code BOM makes sense. I don't know why they'd go through all that trouble to get rid of everything except for a few things. I know its hard to shake off Bollywood as a title, I don't think Mumbaiwood or Mumwood has the same effect on hopefuls trying to make it big in the movies.
In my world Mumbai and Bombay have been two separate places sharing the same space on the map. They exist equally and yet are two separate cities. It will be interesting to see the two cities in person.