Can an account be opened in the name of a sole proprietorship firm?

No, an account cannot be opened in the name of a sole proprietorship firm with Zerodha as it is not a separate legal entity like a partnership or corporation. However, an account can be opened online in the proprietor's (individual's) name. See How to open a Zerodha account online?

Did you know? The bank account submitted while opening an individual Zerodha account can be of the sole proprietorship firm if the bank proof, i.e. cheque or bank statement, contains the name of the proprietorship firm and the proprietor. If it does not include these details, provide a proprietor registration certificate or a confirmation letter from the respective bank by creating a ticket. See the sample confirmation letter format (PDF).