I reckon in time he could easily become a part of your family.
I count "my little family," as DP, DD and myself. They may not be father and daughter, but they still have their own little relationship that is special to them. DP feels protective of DD... I suppose as an Uncle might of his neice. Not the same as if she were his own child, but he's lived with her since she was 3... and she's nearly 7 now.
There are times when I go out and just leave her with him, or he'll be like, "I'm going to the tip, want to come?" (What is it with kids loving the tip? lol) and just take her out. He even took her to the chiro with him (I dunno why) when I was quite able to have her at home with me... so they have their own little relationship. A lot of is it based on teasing and mucking around... but there is discipline there too. He won't put up with her crap, but sometimes he'll even "side" with her when I'm in a bad mood and he realises that she won't have to do much to tick me off... he'll be silly with her and keep her happy and occupied so I don't crack it.
He went out and just randomly purchased her a new bed a while ago - a big expensive one (one of those ones with a desk underneath). I would have gotten her a cheap $200 frame... but nope. So I mean, that's a lovely, unexpected thing he did... and something that made me feel very grateful about. It means she matters to him.
It takes time, but I think Benji and her partner have a "little family," too from what I've read... there's no reason why your new partner (or any long-term partner in future) can't be a part of your family. Not all families are simply biological parents and their children... families come in all shapes and sizes.
I think people would know DP wasn't DD's father if they weren't told.