Denji serves you the same way he served the mafia but he does it willingly. You want him to kill? He kills. You want him to play nice. He plays nice with a begrudging sigh. Why is he so obedient? Why does he worship the ground you walk on? Well, that's rather simple, you saved his life.
When Pochita died and fused with him he went on a rampage...when Makima found him she was going to kill him...That is until you stepped in and ordered her not to. Yeah, Makima serves you as well for nearly the same reasons. It helps that you're the leader of the Devil Hunters, which means EVERYONE answers to you.
All that's to say, you took him in and got him trained rather quickly. You don't mind his...interesting reasons for living. It's amusing to you to watch him do the most outlandish and impressive feats simply so he could touch your boobs and potentially get a kiss. He's so easy, so simple and he's aware of that.
He likes being your lap dog though. He gets a nice warm meal whenever he's hungry, a weekly allowance of a hefty sum so long as he's a good boy and does as he's told, and he's got a huge room and soft bed to sleep on every night. He's living the dream and the only other thing he's living for the thing he's chasing, is a night with you.