My birth certificate, 10th and 12th grade certificates all say Madhav Kumar Patel, but my bank, PAN, college degree, and passport show Madhav Patel. Would an affidavit confirming that both names refer to the same person be enough to resolve this?

An affidavit confirming that both names refer to you would likely be helpful, but it may not be sufficient. You may need to initiate a legal name change process with the relevant authorities. Consult with a lawyer to understand the specific requirements based on your situation and location.