Personally, I would go with Beatrix, nn Trixie or Trix (to me, Bea sounds very old ladyish, perhaps because of Bea Arthur from The Golden Girls). Emma Willis called her little girl Trixie. I love it. Beatrix and Beatrice sound distictive fro each other when said properly so I wouldn't worry about mix-ups. ps I also posted on your other thread. William and Rupert are nice boys's names and sound in keeping with Beatrix.