I do not agree with your Headmaster. In the PAN card, AADHAR card, etc., your father's name is different than what is written in your Xth school certificate. If you do not rectify it immediately, this discrepancy may cause various complicated problems in future.
I feel that you have passed Xth Board examination very recently. So, you can easily submit an application to the Board to rectify the mistake (in your father's name) along with supporting documents (PAN card, AADHAR card, etc. of your father). Most probably, the mistake will be rectified.
However, if the mistake is not rectified, you have to sign an affidavit before a first-class magistrate of your city and publish classified advertisement in one English and in one vernacular newspaper indicating the correct name of your father. You have to preserve the affidavit and advertisement permanently.
Beware! I question everything and everybody.