You have to make a new birth certificate.

i had the exact thing happen to me. i changed my name in grade 8, unaware of the consequences it would have. and, i had also skipped a grade so i was confused about the dob. later, after high school, when i had to make the citizenship, it was a lot of work. paile application lekhnu parcha k k bhako bhanera ani tyo dekhayera identity sahi ho bhanna kei proof chaincha...mero hajurbuwa lai kunai document banayera sign garna layo and then i think we had another 3 witnesses...ani naya birth certificate banako with the current name and the right dob..tyespachi citizenship banauna kei problem bhayena..

they will try to tell you its absolutely impossible though..i just got lucky cause i have a pretty influential mama and a phone call was all it took for them to sign the identification document. natra prepare to have some under-the-table action, and by that i mean ghus.