Let's see ... Christopher Columbus set out to find the westward path to India because to go arround Africa was dangerous, and the path overland was slow and hard. He had miss-estimated the size of Earth, so when he finally arrived in North America days after when he though he should have found India, he was sure he must have finally reached India; because of this, he referred to the natives as Indians.

So....since the whole point of the journey was to get to India, yes India had been discovered before that point. Since he called the natives Indians because he thought they were in India, it would be logical to assume that the inhabitants of India are called Indian, even if you don't know what all the people groups of the world are called.