No surname in birth certificate

[Prettypoppy]

I will be applying for green card soon and I just noticed that my birth certificate has no surname but only my first name (with a missing letter). To get a new birth certificate with correct name, it is a very long process and the authorities require original passport for proof of name. As I am in US and my parents will have to get this done in India, I am not sure how they can provide my passport for proof. 

Will the current birth certificate be ok? I am not sure who to check with? If not, is there any other document that can be given instead of birth certificate? 

Please advise. Thanks.