Second Filter
Not sentient, no. That would lead into some rather questionable areas of magic. I wished I'd examined the hat more closely when it was here. It really is unique. Most similar artifacts that work on an identity principle are much more limited, but this isn't about recognizing ownership. It's about personality, character... I think you're right that the simplest method would be some form of question and answer, disappointingly formulaic, but likely better for practical purposes than actually reading minds. It doesn't preclude attempts to steer the results, however.