Document verification by UPSC.

Yes. UPSC will accept the affidavit. If there is a name change in the certificates it will create problem and UPSC may object for that. As you said that CBSE is not accepting to correct your name in the 10th certificate, it is important to go to a lawyer and get the affidavit made and get ready with that before you go for document verification. It is very important. Otherwise, you will be in a problem.

Your name is incorrect only in 10th mark sheet but it will create problem in the document verification not only in UPSC but anywhere else also. Your board office has refused to correct it. Now the only option is to get a legal affidavit prepared. You have to take help of a lawyer in this regard and get an legal affidavit prepared where all those details are mentioned and a copy of the supporting documents is to be attached with this affidavit and is to be signed by you in presence of a magistrate or authorised notary public authority. He will also countersign it under his seal and that document is to kept by you to show at the time of document verification.

Once the document is prepared by the lawyer, please cross check it thoroughly and see that there is no spelling mistakes in that about the entered details otherwise it will lead to utter confusion at the time of verification. Please note that this type of legal documents are in the nature of taking an oath and should be error free as their specific purpose is to cover and explain the errors in some other documents.