Ok what should I do about this guy?

Ok so I have a daughter Samrie and her father and I broke up about a well 2 months ago... It was pretty hard considering the fact that we're both teenagers and Samrie was well attached to her daddy. So this guy named Mathew (Mateo) came along and we've been dating about a month now. We're pretty serious, but he hasn't met Samrie yet. He wants to but i wont let him. He respects the fact that I don't want him to be around Samrie yet considering her father and I just broke up and she's 2. The reason being that I don't want Samrie getting attached and then never seeing him again and I'm just not comfortable yet. Mateo talks about how he loves me and all and will still love me even if he never meets Samrie. I'm wondering should I let him see Samrie or should I just carry on with our relationship till I'm comfortable. I don't want Samrie to start calling Mateo Daddy and everything because that's not her dad... her dad's name is Antonio. What should I do about Mateo?