x-posted....wanting to figure this out (guardianship/legal father?)

Ok now that L is almost 4 and starting to be eligible for extracurricular activities....we just signed up for soccer, yay! and next year is school....I wanted to ask a legality question.... As of right now, been married for about half a year, so we are waiting a while before doing anything more formal like S adopting L through step-father adoption or second parent adoption....whatever, but as of now, she does not have a legal father.....obviously TPR included her bio mother and father, and I adopted her as a single woman....now that I'm married, S is great with L and treats her like his own....so when applications come about, I just feel like putting his name under "father's name" etc. Can I put that he is the legal father since he married into a different situation so there is no other father in the situation with rights? or does there have to be some papers even guardianship type for him to be considered a legal father....does my question make sense? Thank you. or should I just put his name on the father side and then deal with questions later if they see that his last name isn't the same as L's? we would like L to be more cognizant of the adoption process so if this second parent adoption happens, she knows and is aware of it and can choose if she wants to hyphenate her name, keep it, or change it to his.