I think a reissue without name is different from change of name. An affidavit for formally change your name should be sufficient, but again this is an INZ discussion, so it dfepends on their position, because this will not result ina new birth certificate, and as I undersyand they are discputing if the academic records belong to the same person given that the submitted birth cert has a different name on it.
In Calcutta you can apply for a "Same Name" certificate, to account for spelling differences, not sure about other parts of the country.