1. You shall have to execute an affidavit affirming that your name has been wrongly mentioned in your certificate awarding you the master's degree as such and such in place of such and such which is your actual name and also that the authority issung the master's degree certificate are required to correct the error and issue the certificate afresh with your correct name.
2. Thereafter you shall have to publish the gist of the affidavit in the Gazette and two Newspapers one being in Vernacular.
3. Finally you shall have to write to the authiority issuing your master's degree for issuing the said certificate afresh with your correct name.
4. Your problem will get solved now and you can apply for your passport in your corrected name.