Name correction on CBSE 10th Certificate to get the Government ID

Hello, I completed my 10th from CBSE in 2003 and when I got my result I realized the name correction and told my father about it, but he did not take any action about it.Even I did not knew any rules and the time period to get it corrected. Its been 14 years and now I am facing the consequences of not getting it done. In the certificate my surname is not Included before my name and below to my name father's surname is mentioned. Now, If there is no possibility to do the correction then can I go ahead with the name mentioned as on 10th Mark sheet for all the Govt ID's proofs? I am very confused over this. For ex. My name is NV - First Name Last Name as mentioned on Mark sheet and my Father's Name is ("Karri" - Surname) First Name Last Name. In fact "K" should be included and it is absent. If I get the Govt ID's Created per the corrected name and my certificates are not corrected will there be any problem. If any problem arises what kind of problem would I face. Please guide me to be in compliant with Law. Also, because of this incorrect name all my Govt ID's are with different names and a result my passport process was kept hold.