No. Veganism is yet to catch on in India so there isn't a word for it yet in any Indian language. However, you can use the English word 'vegan' and will probably be understood in tourist places and most upscale restaurants in urban India.
Otherwise, you will have to describe veganism. शाकाहार is traditionally understood to be lacto-vegetarianism in India (ie, vegetarianism without eggs). So, you can say मैं शाकाहारी हूँ और मैं शहद, दूध और दूध से बना कोई पदार्थ (जैसे दही, घी, मक्खन और पनीर) नहीं खाती। (I'm vegetarian and I don't eat honey, milk and milk products (like yoghurt, ghee, butter and cheese)).