The areas that work without any trouble: Mahipalpur and Aerocity at the airport, Paharganj opposite the station, Karol Bagh behind the market. Those four are built on this trade in one form or another and nobody at the desk is interested. Gurgaon works too - the Golf Course Road hotels are business hotels with key-card lifts and staff who have seen everything.
The area that genuinely does not is Chandni Chowk and the old city around it. The hotels in the walled city are small, family-run and frequently will not take an unmarried couple at any hour. That is not a licensing matter, it is simply who runs them, and no amount of asking changes it.
South Delhi is in between. Green Park, Hauz Khas and Saket have very few hotels of any kind - they are residential colonies - so bookings there are to flats rather than rooms. Press Enclave Road in Saket is the exception.
The general rule worth carrying: a hotel that asks for identification is not refusing you, it is doing what the law requires, and a hotel that asks for nothing at all is often the one with other problems. Give the hotel name when you ring and somebody here will say straight away whether it is going to be awkward.
The addresses page says what each part of Delhi does to a booking.