conversion of OPC to pvt. ltd.

Conversion into a private limited company is not permitted unless two years is expired from the date of incorporation of the OPC.

If it is more than two years of the OPC then you can simply convert it into private company by filling an application to the registrar along with a copy of the resolution.

Converting to a private limited company, OPC is required to have 2 directors & 2 members.

You don't need to apply for new name.