Hello Sourabh,
You need to get it rectified as soon as possible. Ideally, you should be using the details provided in your PAN or AADHAR, but since you have a different name of your father in your educational certificate, that might become a problem later on. Kindly get an affidavit made which you need to sign before a first class magistrate of your locality. Please approach a lawyer for the same, they will make the process easier for you.
Let us know in case you have other doubts.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile