I don't think him having my checking account number, name and address gives him full ability to steal my identity. He could print bogus checks, however. If that happens my credit union will fight those charges for me and I'll close that account.
I've only once in my life had someone write bogus checks against my account and that was largely my own fault. I forgot my checkbook on the passenger seat of my old Austin Healey which had no door locks. Within a few days I received a phone call from the one local grocery store we had in the little mountain village I lived in. I immediately went to speak with the manager. He demanded that I cover the bounced checks which he showed me. They were all written for very small purchases plus $100-200 cash. I told him those weren't my signatures. He said I still needed to pay for them. I asked if he could tell from the checks which cashiers accepted the checks. He said, he could. Since I was the only photographer in that little village many people knew me. It turns out all three checks were initialed by the same cashier who was working that day. The store manager and I approached her and she said (very sheepishly), "Hello, Mr. XXX", then glanced briefly at her boss then her gaze went straight to the ground. The manager said, "Never mind, Mr. XXX. I'll take care of this".