I Am Not My Animal's Owner. So What Am I?

My wife trapped a stray cat (Bob B) in our rental house three months ago. I’d lived with cats for a long time and had some luck in training them so it seemed like an adventure to start from zero.

For about two months he would not recognize me, eventually I got him to walk halfway across his shelf to eat a treat but he wouldn’t come down to the floor to eat his meals even though he seemed to be moving around as if he was thinking about coming down.

I had decided to only have the food out when I was in the room but when I approached the food bowl to take it away he yowled at me. It was a breakthrough because he started communicating with me and asking for things as if he realized the path to a better life went through me.

I’m not sure if he thinks he is my cat but I think he accepts me now as “his person” and along the way I became strongly attached to him even though he still won't let me touch him. I’ve thought a lot about what our relationship is and I think it’s a lot like I’m his boss in some sort of a gang. I think he understands he’s under my protection (are we like a feudal lord and his vassal?) and he’d expect me to back him up in a fight (see it in his body language as he explores an unfamiliar space.)