I just replied to a 485 RFE for birth cert w/o my wife's name
Most applicants don't see a RFE for the name not being there, but its not impossible. I got one, have seen others.
My suggestion: Go ahead and apply with hospital certificate plus affidavits from parents/relatives. On the background, keep working on getting either a new certificate from municipality or a non-availibility certificate from the municipality.
Else wait to get a new cert from municipilaty and then apply if you want to be extra careful. Getting certs out from municipality takes time/effort unless you have contacts. YourmanInIndia.com does this for a fee. I got them to get a new cert from bombay Municipality to include my wife's name (the original one didn't) by paying 50$ and sending e-mails every alternate day in a month's time.