Currently on an iphone family plan under his name?

My recent boyfriend had an upgrade on his plan so he took me to the at&t store and got me an iphone under his name and now we have a family plan. For personal reasons, I'm moving back with my parents and broke up with him. He wants me to keep the iphone but I'm uncomfortable with the fact that I'm still under his name and that he's paying the phone bill. It's a 2 year contract so I don't want to pay the price of the phone to cancel my line. Can he see who I message and what I do from his account online? Is there a way to keep our phone activity private while being on the same plan?

Just be real and ask him