For instance, if you have a Gabrielle, you might call her Gabby. My daughter's name is Caroline, but we're going to call her Carly. Now as a parent, that is entirely your decision.
But have you ever encountered someone shotening your child's name even though they go by their full name?
A friend of mine's daughter's name is Madelyn. She calls her Madelyn, and she didn't realize it before she was born, but the name Mady makes her cringe. Everytime her daughter is introduced, she's introduced as Madelyn. However, a lot of people take it upon themselves to start calling her Mady. It drives her nuts!
I guess if a child was introduced to me as a certain name, I wouldn't go changing it unless I heard the parents or the child theirself call themselves by a different name. Maybe that's just me?