Mumbai (was Bombay)

[topaz]

Christopher Hitchens argued this week in Slate that Mumbai (the name for the city known as Bombay until 1995) is a "fake name," compares it to the Burmese junta renaming that country "Myanmar", and suggests that right-thinking people will continue to refer to Mumbai as Bombay.

I don't get it.  The opposition in Burma to the name "Myanmar" is partly a symbolic opposition to the military regime.  The Burmese protesters do not even recognize the legitimacy of the ruling party.  I don't see that the same issues apply in India.  As evidence, Hitch cites this 2006 Slate article by Christopher Beam:

Shiv Sena's leadership pushed for the name change for many years prior to 1995. They argued that "Bombay" was a corrupted English version of "Mumbai" and an unwanted legacy of British colonial rule.... The push to rename Bombay was part of a larger movement to strengthen Marathi identity in the Maharashtra region.... The name change didn't impact all of Mumbai's residents. Speakers of Marathi and Gujarati, the local languages, have always called the city Mumbai. "Bombay" is an anglicization of the Portuguese name "Bombaim," which is believed to derive from the phrase "Bom Bahia," or "Good Bay." (Portugal held territories in western India until 1961.)

So at least to some degree it's a top-down change.  But it's not clear to me that that automatically means that "Bombay" is a more proper name.  Why is a 16th-century Portuguese colonial name more culturally appropriate for an Indian city than a Hindu name that derives from local temples going back thousands of years?

Help me out.  I know a lot of you are smarter than I am and pay more attention to Asian politics than I do.  Am I missing something big from the backstory here?