How to name corrected on class 10 Certificate for Govt ID correctly?

Hello, I passed my 10th from CBSE board in the year 2003 and there was a name correction in my name. I noticed it and informed my father about it but he did not take any action. Now, after 14 years, when I want to get the correction done, CBSE rules says it can be done only within one year of result declaration. Now, if there is no possibility to get the name corrected on the mark sheet, what is the other way to get it done. If I have to continue with the name as on Mark sheet then my surname is not included in the Certificate. If I get the Govt ID proofs as per the corrected name and my certificate is not corrected then will there be any Problem. FOR instance- My name as on 10th Mark sheet is NV xxxxx xxxxx and my Father name is Karri xxxx xxxx. Here Karri is surname and Karri is not added to my name. If I get the GOVT ID created by name KNV xxxx xxxx and my 10th Certificate is left like that is it okay? I am very confused over this Name glitch on my Mark sheet for creating ID's.