My husband would like to adopt my daughter. Her biological father is unknown and on her birth certificate there is no one is the spot of FATHER. How do we go about getting her name changed and him as her father on her birth certificate?

Well unless you are MARY and the baby is JESUS the child had a father even if the name was left off the birth certificate.

So you have to show where you tried to find the real bio father and if they can't be found there is laws for publishing a notice.
Since the real father where ever he is, even if not listed on the birth certificate has legal rights, and the court will have to see that every effort is made to find that person.

He will have to adopt the child to be put on the birth certificate.