Your off a lil, Michael says your family is still called Corleone. TB is right, Michael gave Pete the family but out of loyalty to Michael(and out of awe of what he just did) he never broke off from the Corleones like was planned, this is shown when he is kissing Mike's hand at the end calling him Godfather. TB is right like he is mos the time, NY was under Mike on a long chain then a shorter one.
