Phone rang, Facetime identified my daughter as the caller. I answered, but it was not my daughter. I saw the caller. Once the caller saw me, she freaked out and hung up. In my "recents" the call was identified as from my daughter. What's up with that?
Something similar happened to me one time. I made a FaceTime call, and it connected to a complete stranger. We both freaked out.
I had an old, stale cell phone number still attached to the person I was calling. I suspect, but could not verify, that the number had been re-used and the new owner attached it to a different Apple ID. FaceTime decided for some reason to place the call to the wrong Apple ID.
I deleted the old phone number. Since then, I've never had any trouble making this FaceTime call.
You only need your Apple ID to register for Facetime, so it sounds like one of your daughter's friends was playing around with her iPhone/iPad/iPod/Mac.
Or your daughter sold it, and forgot to log out of her Apple ID before handing her device over.
Another scenario could be that she logged into Facetime on a friend's Mac with her own Apple ID, and it's still logged in.
Could any of those situations be it?