Is Bitsy short for anything? doubt it - usually a name just fits - some are nicknames and others are their given name - over the years I have known or have been friends with: Artie, Ibby, Rafe, Izzie, Bambi, Pepper, Jo-Jo, Kissy, Sister, Bo, Cricket, Tiny, Tip, Dee, Duke, Ezz - then there is Tuck, Trey, Ty, Tex and Tank as well as, the well known philanthropist from the Houston Hogg family - Ima Hogg - myth had it that she had a sister Ura but that was just a myth.
That is not even touching all the double names like Joe Abbott - Alma Grace or girls who are Miss this or that or Lady this or that as their name not just a polite salutation - Lady June - Miss Mary Morgan followed by their sur name example; Miss Mary Morgan Schade
And then with a large Mexican American population we all know a couple of boys named Jesus, or Chantico; Girls named, Anacleta, or Palla