At the moment it's laid back because at the moment he isn't paying ££££ for a rental for you plus whatever other expenses you will charge him for.
Once he is paying more there is a strong possibility that he will expect more, and rightly so because he is paying a premium for this and will want his money worth. Maybe not now but soon, as at the moment he has you in a false sense of security. And yes a false sense of security because you don't seem to understand how this can go wrong. Just look at how you answered the valid question of what happens when he is horny and you aren't. This would be a concern for any sugar baby, or it should be. If this doesn't concern you, or anyone in the same position then this is alarming.
But you seem to have already made up your mind and will be moving into a rental solely in his name, where you can legally get kicked out by him at 3 am. You are putting yourself in an extremely vulnerable position in terms of homelessness and sexual abuse/exploitation. Get saving now for that emergency hotel you will need, and the deposit etc for when he boots you out when you utter the words, No I'm not horny.
I am not being negative. I am being realistic. Relationships break down every single day, even casual ones, and the person who loses out is the one not on the paperwork.