Second name addition in share certificate

I am share holder of a public company. holding physical shares of the same company. problem encounter during dematerialisation is as follows :

1) Share certificate is in the name of first holder.

2) demat account in the name of first and second holder.

Problem : is the DP would only accept demateralisation reqest if both the names are mentioned on the physical certificate.

Tell me how to go about it ?

1) Does the dematerialisation require such an arrangement please quote the relevant act and section?

2) If the above is true then what is the procedure to add the name of the second holder name in the physical certificate.