Birth certificate snafu

[kohsaphoenix]

My current birth certifcate has my name as 'Arun' where in my passport the "Given name" is "Arun" and Surname is "Selvaraj Kuppusamy". Do i need to get the birth certificate with both my "given name" and the "surname" as in passport? (Arun Selvaraj Kuppusamy) for green card application . My class 10 and 12th and degree certificate has my name S.K Arun.

Please help