We would like to do a step parent adoption but we are afraid that would be when he would want to reappear just because my husband wants to make it legal.
He could want to reappear at any time anyway.

As it stands, he hasn't legitimized her, doesn't pay support, and has had no contact - all pointing to abandonment, which would make a step-parent adoption pretty much a slam dunk.

We don't want to get her involved in all of that.
Let's look at it another way. You do only the name change, no step-parent adoption.

Two days later, you are killed in a car crash. Your husband is legally NOT the child's father. He has zero rights to her. Bio Dad can show up, petition to establish paternity (he'll get it), then take the child and your husband will never see her again.

Still want to maintain the status quo?