I had a chat with one more guy and he says that it might or might not be a problem, there is no written rule that you can do this. It all depends on the person at the counter which is a slightly stupid answer. But if you look at the situation then even if I dont get a new passport from India even then I have two different names as in old passport its(Siddhant) and in Permit it will be(Siddhant Siddhant)