Until the British colonised that part of the world, India didn't exist as a single nation. Each of the regions were self-governing, with their own conventions about things like names (which might be interlinked with both religion and caste).
Many of the regional differences exist today (although generic names have come to replace many caste-based names), so the way that an Indian player uses his name depends largely upon which part of the country he comes from.
See here:
http://en.wikipedia.org/wiki/Indian_name
Chris