Amplify Department of Information Technology and Management, Bharati Vidyapeeth University

Primarily because it is an administrative headache (not an impossible task, just another painful task for people who are already overburdened)- and the people there (inside IITB) don't care as much about the issue as the people from the political parties that want the name to be changed. They really do want to do better and more productive things than to pander to the whimsical desires of politicians on this name-change brouhaha.
Either way, it isn't IIT Bombay's prerogative to change its name to whatever it wants. Considering the legal status of the IITs, any change of name has to take place through an act of Parliament as an amendment to the IITs Act[1]. There was some talk about an amendment back in 2008[2], but nobody really knows (or cares) about what happened of it.
Interestingly, IIT Bombay is not the only entity to not have been renamed. The Bombay Stock Exchange and heck, even the Bombay High Court have not been renamed. Over in Chennai, IIT Madras retains its old name.