The name Liz is a girl's name of Hebrew origin. Liz and is often added to lists like Nicknames for Elizabeth and discussed in our forums with posts like "A brother or sister for little Jack or Olivia".
From the experts:
A girl named Liz on her birth certificate could feel deprived of her full identity. Call her Liz, but name her Elizabeth -- or at least Lizbeth or Eliza.