The name on the share certificate should match the name on the demat account. In the case of name mismatch, you need to submit a Gazette letter or an affidavit on Govt stamp paper stating that name on the share certificate and name in the demat account are of the same individual.
If you have shares of more than 1 company then you need to submit the notarized copies of the affidavit/Gazette for all the companies.