Change mother's name on birth certificate

My son was born in Dec 2016 in Nagpur Maharashtra. Her mother's name (My wife) on birth certificate is typed incorrectly. My wife's all documents have her name as one before marriage. My son's birth certificate has my wife's name as her name after marriage(the name which is on none of my wife's documents.) We ignored this as we thought we will change her name later and we need not change the birth certificate then. Now we have applied for passports for both of them.My wife has applied and received passport with her before marriage name. We mentioned same name in my son's passport application but my son's birth certificate has her name as after marriage(Again which is on none of the documents) So my son's rte application is stuck and objection has been raised by Regional Passport Office. How to get the name corrected on birth certificate? We wish to update birth certificate of my son to reflect my wife's name consistent with her documents. Also how long will this process normally take?