Please make it sure that your name is reflected correctly in your Marks sheet or Pass certificates. If they are accurate, there won't be any problem even there are some minor corrections needed in father or Mother's name. A stitch in time saves nine. Any correction in the certificate needed requires authentication by the CBSE or the State Board as the case may be. You have to approach your school/college first who would route it to the Board dully vetting your application. When things are delayed, there may be some hurdles due to laxity or technical reasons and in such extreme conditions, you need not be worried. A legal affidavit duly signed by the Notary would always be a good option .
This is the process in every case whether a clerical post in Government or an IAS probationer. Because your character and antecedents would be verified by the IB or some other agencies before issuing appointment order. In such cases, the parental details would be verified. Don't worry. Try to change the name through Board itself as there is no bar and you can approach them at any time even after a lapse of one or two years, be sure with your Registration particulars and enrollment details.