Wrong name on newborn’s birth certificate.

We didn’t notice that our newborn baby’s birth certificate has the wrong name until we are trying to apply for passport.

He is currently 6-7 weeks.

We are surprised that we didn’t notice that when the hospital staff talked to us and confirmed with us for our baby’s birth certificate…

We are in California Santa Clara County.

How can we change the baby’s name on birth certificate and SSN card quickly?