Lol.. I dunno what wood you blokes call what, Bollywood, Mollywood, Morningwood.. Anyway it's just a pretension to Hollywood in the first place..
But thats beside the point if it's the wish of Shiv Sena to change the name to Mumbai in some nationalistic fervor, Change everything thats synonymous Bombay as well and that includes Bollywood.. Why keep names that works for you, It's hypocritical to pick and choose.. Actually most non Indians and lots of expat Indians too still refer to the place as Bombay.. It will take another generation or so for Bombay to loose it's usage, If it ever does
Again it is our choice .
Still people may Bombay but officially it would always known as Mumbai .
SS is political party in a democratic nation .If they are ultranationlists then it is their right within constitution .Noone can ask question to them about that .