Need help about my issue in Cast Certificate Document For UPSC

The best course of action is to make an affidavit and then get the information published in the Gazette.
You can contact a local lawyer known to you. You can discuss this with him and make an affidavit and get it signed in presence of a judge. Once the affidavit is made get it published in two newspapers saying that Vijayan and Vijayakumar are the names of the same person. You have to refer your affidavit in the advertisement. Your lawyer will guide you in this aspect. One newspaper should be an English newspaper and the other one should be your local language paper. Once this is done, keep the originally advertised news paper cuttings with you. Then apply to Gazette for publication of this information in the next issue of Gazette. You have to apply in the format that will be provided online on the website. You have to attach a copy of the affidavit and also copies of paper advertisements and the required fee. You can get the required guidance for this also from the lawyer. Once this entire process is carried out you will not have any problem and you can continue with the same certificates.

Any variance in respect of name and the other entries in any certificate needs to be corrected so that all your certificates are free from discrepancies. This is essential in all sorts of interviews or for procurement of higher studies.
In the present situation, take the advice of the lawyer so that an affidavit can be procured either from the Notary Magistrate or the First Class Magistrate. The lawyer would assist you in the preparation of the draft and the same would be signed by him where your signature would be required in the left side of the Affidavit Certificate. Your signature too will be attested by the Magistrate.
Now the next step would be to get the published in two news paper - one being the leading English News Paper and the other one would be the local paper. Get the same published as per advice of your lawyer. Preserve the cutting so that the same could be produced before the documentation authorities whenever required.

Change in the name is always a perennial problem as it hinders in the verification process and no one will accept a mismatch in such a vital data. That is why we are always advised to give the correct name consistently everywhere when we go for registering or applying for any course or Govt certificate like Aadhar card, Voter card, PAN card, caste certificate etc. Anyway mistakes happen in our lives and we have to take the corrective measures for that.

First and foremost thing in this respect is you first check as what is the correct name of your father that is as per his birth certificate or Aadhar card or any document which can vouch for it. This is of primary importance and then you have to try to get the name corrected in all the certificates wherever it is misspelt or wrongly mentioned. Now, that seems a big exercise and some of the offices might not in cooperating in that way so the only recourse available with you is to go for a legal affidavit and publish this thing in local newspapers as well as get it notified in the Gazette of India. There are standard procedures for doing that and you might have to take help of a lawyer who can get the things done in a smooth manner. The affidavit is to be signed by you and is to be countersigned by a first class court magistrate.

Please note that you have to make copies of the all the relevant certificates which will be mentioned in the affidavit and will be annexed with it and make a part so that anyone can check them for a cross reference.