Putting boyfriends name on house??

Me and my partner have been together 5 years and have 2 kids, I will say that we definitely need to work on our relationship and he has some problems on his end that we are working through (commitment issues and porn addiction). My mom bought us a cheap house that needed work, we’ve lived in it for a year and are selling it. I did most of the work but he did about 35%, and because it was fully paid off he didn’t have to pay a mortgage or anything like that while he worked and I stayed at home with the kids.

I’ve also paid a good amount of bills with my savings. Now that we’re buying a nicer house with the money we get for selling this one, he wants his name on the new house.

We’re not married (even though I want to be), and he doesn’t plan on it any time soon. My mom really doesn’t want his name on the house, especially because it’s all I have to provide. He has a bunch of family and friends over here and I have absolutely no one, so if we separated he could stay with a bunch of people and I wouldn’t be able to stay with anyone.

But I know he’s going to like this idea and think I don’t trust him. I don’t know what to do.

Edit: Im getting enough money from my house for the new one so I won’t need a mortgage.