It's natural for your daughter to want a Dad. But your boyfriend is not her Dad in any sense of the word. Calling him Dad will not in the end make her happy. She wants someone who is in her life much of the time, who does Dad things with her, who is more than a friend. Therefore, if you don't want to get married, he can't be her Dad. I think that is what you're saying.
Definitely do not get married so your daughter can have a Dad. Is that what you're asking? If you should? If so, do not! A marriage has to be based on a great number of things and it sounds like you've found that those things aren't present.
He isn't with her enough to take on the role of Dad. He could show up for school events that include fathers and call him Dad for that event. But it's important for her to know the reality of the situation. He's not in the role of Dad.
I say this even tho my adopted daughter accepted my so as Dad. She didn't know her father and my friend took on the role of Dad. Although he didn't live with us nor did he stay overnight, he was with us several evenings and frequently on week ends. He co-parented with me. He felt like and acted like a father. I doubt that I would've been a successful parent without his help.
If you want him to take on the role of Dad then he must be co-parenting with you. To be called Dad he's involved in making decisions. She would be able to ask for his permission and be able to rely on him to be there for her when she needed him. Only then would I let my child call my so Dad.
I take exception to the idea that he would have to adopt her before he could be her Dad. Adoption is a legal formality that can have nothing to do with the reality of the situation. Millions of children call their step-fathers and mom's boyfriends Dad.
Whether or not she calls him Dad is your decision but you need to be sure that you're not confusing her even more if you do that.