A partnership firm cannot open a demat account entirely in the name of a partnership firm.

As per section 2.4.5 of CDSL operating guidelines, while a trading account can be opened in the name of the partnership firm, the demat account must be opened in the names of at least two authorised partners and a maximum of 3 authorised partners. To know more, see What are the documents required for account opening of any partnership firm at Jainam? 

However, both the trading and demat accounts are registered with the partnership firm's PAN, not with the individual partners' PANs.