This wasn't my experience last month, at least for a prepaid data card. I went through extensive procedures in coordination with the (excellent) concierge at the ITC Royal Gardenia and at the end of the day, the phone companies (both Tata and Reliance) wanted way too much documentation.

Hotel arranged for reps from both Tata and Reliance to visit my workplace and the hotel, respectively. At first, we started with Tata and were told that they would only require passport photos, a copy of my passport, and drivers license. Then, we were told they would also require an "official" letter from the hotel, which the hotel provided within 10 minutes. Then, Tata told us we would need a letter from the Police Commissioner, so we started with Reliance. Reliance actually gave us the device, but then later refused to activate it without the Police Commissioner letter.

Requiring me to go down to the Police Commissioner (and probably have to pay him to get this letter) was just too much. Especially considering the nature of my work, which is anti-corruption related.

This process was drawn out over a couple of weeks. FWIW, my own company (an international accounting/consulting firm who gives these data cards to every Indian employee) could not even arrange for one of these in my own name.

Eventually I just gave up, hope you can do better.