any sites other than Zebpay ??
You can use localbitcoins for better experience if you are not satisfied with these exchanges, because you will be able to transact your coins for different available rates and you may get prices even higher than Zebpay sometimes. At these exchanges, you will need to wait for your money to be funded and the waiting time is 24 hours (depending on when you withdraw), while at localbitcoins, users send the funds instantly through IMPS, or 3-4 hours if NEFT is being done.
Even in Localbitcoin you dont have to give your personal details for trading but some time the rates are very different (in the sense rates are too much gap in buying and selling comparing to other exchanges) but other exchanges you have to give your personal details after that you can trade