His enemies liked to refer to Joseph Smith as “Joe.” Some still do. But he seems to have preferred the fuller and more formal Joseph. Likewise, if his father was ever called Joe by his family or friends, I’m unaware of it. There seems to have been a culture of some formality associated with the Smith family names. If Alvin was ever called “Al,” or Hyrum “Hy,” if William was commonly called “Will” or “Bill” or “Billy” or “Willy,” there’s little sign of it. Was Joseph’s sister Sophronia known as “Sophie”? Was “Katharine” commonly called “Katie” or “Kate” or “Kathy”? Perhaps. But the evidence for that seems to be lacking.