Amitabh Bachchan tweeted a few days ago that Shamitabh has no particular meaning. However, those who are well acquainted with Hindi or even other Indian languages, can make some guesses here.
Shamitabh doesn't have an existence as a word, but if you say 'Amitabh-Shamitabh', then it would mean something like 'Amitabh etc.' This is the way many Indian words are spoken in casual conversation, e.g. if you say 'bhoot-voot kuch nahi hota', it would translate to, 'there is nothing like ghost or something' or 'there is nothing like ghosts etc.' or simply 'there is nothing like ghosts'. So the appended part is something negligible, not so important, or completely non-existent, depending on situation.
This way, taking a cue from the title, Shamitabh could be an 'et cetera' with respect to Amitabh Bachchan, and it could well be story of someone relatively unknown, unheard, who is trying to become like Amitabh Bachchan.