I am marrying my boyfriend soon and after, We want him to adopt my daughter. I don't know who her biological father is because of certain circimstances. There is no fathers name on her birth certificate, only mine. What would I have to do?

This will be up to the judge and your states rules. It is possible that they will want or require you to attempt to find the father and get him to sign over his rights.

First of course you will need to be married and normally married for one year ( in most states) you will need an attorney, it is possible they may allow a public posting of the adoption giving the possible father to come forward.