Alright, The demat accounts are held by depositories i.e. CDSL and NSDL. Only these two companies.
However, if you are asking about trading and demat accounts then i will suggest discount brokers. They offer trade for free to Rs. 20 per trade.
Remember, if its free its not always beneficial. In stock market , the diffrecen between free and Rs. 20 isnt much but it greatly effects when it comes to service. a person offering it free wont earn anything as he cant give you quality service. A person Chargin rs. 15 or 20 will get nothing from you but gets alot from all over india so insted of going free, pay upto Rs. 20 to your broker.
There are multiple brokers such as zerodha , Fyers, tradesmartonline and others too. However, we have dealt with zerodha and tradesmart and their performace is great.
Google pros and cons about any brokers by googling it. Here you will find marketing people prasing their company. You can read about few discount brokers in my website www.dematguru.com Exciting Offers On Opening a Trading and Demat Account – Demat Guru
If you going for IPO then also you will need a broker to sell your shares so consider one from Exciting Offers On Opening a Trading and Demat Account – Demat Guru but for revies, do google.
Welcome to market.