Your fiance is a legal stranger to your daughter. Right now he isn't even a step-parent.
The bio father could contest an adoption procedure or maybe he would be willing to give up his parental rights. However, right now Florida doesn't even recognize him as the legal father. (That would still need to be established.)
Fiance can not just get his name added without the two of you making a sworn statement that he is the biological father or perhaps even a court order to do so, and as pointed out the prior would be fraud. You both know he is not the biological father.
A step-parent adoption would be the legal way of handling this. There aren't any short cuts.

