We have a defined template for SRS & DDD in our organization. For some of the projects, the customer is providing the requirements and hence they are using their own template and format. Kindly clarify whether we can accept this modification / removal of the existing approved template in our QMS.
You haven't indicated at what level of CMMI your organization is performing at, but it sounds as if your customer is providing an alternative to your "standard" template that projects are expected to use.
Both OPD and IPM provide for the introduction of new or alternative "process assets" that are introduced at the project level, and this situation is one of the reasons those SP's exist in the model.
Assuming that projects know this at the beginning, and that this was planned for in their Configuration Planning, AND your tailoring guidelines allow for it (if you're ML3 and you have tailoring guidelines) AND the customer-provided template has all or most of the attributes required (such as traceability) then this is a perfectly acceptable alternative.
As a matter of fact, successful demonstration and management of this practice shows a higher level of process maturity than forcing everyone to use the same document regardless of the situation they are in.