It will primarily depend on the extent of variation or mismatch. Without knowing the exact details specific comments cannot be offered. However, in case there is no intentional error or a fraudulent objective, solutions to most of such issues are likely to be available. Generally, a sworn/notarized affidavit serves the purpose in most of the cases.
In my opinion, the author should study the website of the 'Passport Seva' - http://www.passportindia.gov.in/ thoroughly and may consider submitting his application also for obtaining a passport in his name by observing the due procedure given in the guidelines. In case, he is unable to understand the same, then help of some other person may be taken for understanding the same.
Once the passport will be ready with the actual name of the author and his father then the same can be used as ID proof and the address proof in future. Alternatively, the author may get his Aadhar Card and PAN card also prepared with the correct names by observing due procedures regarding the same.