You did not mention where her father is and if he is involved in her life.
I agree with your boyfriend. She should not be calling him daddy unless he adopts her. There are several reasons for this, one is that he is not her daddy. You have been together 9 months, what if, by chance, you break up? She will be devastated and it will really affect her emotionally. Children take everything serioulsy and to heart. They also get hurt very deeply and most of the time they think that whatever goes wrong is their fault. Secondly, you should not pressure him into this either b/c he may get scared away. No man wants to come into a relationship being told he is to play daddy when he is not their daddy. I don't think he is saying he does not want to take care of her when you are married, financially, or otherwise, I think he just does not feel comfortable with a child calling him daddy when he is not her daddy. Give him time as your husband and it will come naturally.
She is 5 yrs old which is now old enough to learn a little bit about her real daddy. Not deep details of course but you can tell her that when two people are in love, they make a baby but that does not always mean that they stay together forever. Sometimes they fall out of love. Sometimes mommies find another person to love and that other person can sometimes become your 'family' but that does not make them your daddy. You will always only have one daddy. This does not mean that ??? does not love you, it just means that he did not create you with mommy. He has his own children and they have their own mommy. You wouldn't want his kids to call me mommy would you? I am your mommy and he is their daddy. When we get married, he will be your family too and he will do everything that daddies do, but he is not your daddy....???? is. It is not fair to her to think one thing and then years later find out another. You can give her bits and pieces of info as she gets older but she does need to know the truth, little by little as she is age appropriate.
Later, if you get married and he decides he wants to adopt her, you sit her down together and tell her that you are all now a family and that ???? has asked if he can adopt you. This will make him just like a daddy and he will be here for you and for mommy forever.
You must be very careful with a child's feelings and emotions. Although it will make you happy to have a daddy for her, you have to think of her. You take care of her as if you were single b/c technically, you still are. Don't get her so close to someone until you are married.
If he has a "short patience", you might need to work on that before you marry him. That is not a good trait to have, especially around a child. Take care of her, keep her in as little of conflict, emotion, etc as you can. Everything a child encounters when they are young is forming their personality later. It is amazing to watch and see what affects them and how. Keep happiness in her upbringing, patience is huge in raising a child. Teach her patience.
Good luck, let us know how it goes.....