Do you think someone will take a grown man seriously when he says his name is
Billy or
Stevie? I wouldn't-- it sounds childish and your baby won't be a baby forever.
Many names, like
Alexander,
Zachary, and
Matthew, get shortened to their nicknames automatically-- I can't tell you how many times a teacher has taken attendance in a class and come to a
Matthew and asked "Do you go by
Matthew or
Matt?" It's only "different" nicknames that would have to be corrected (Like
Xander instead of
Alex,
Liam instead of
Will or
Bill)
So-- basically, no. Give them a full name and call them by a nickname if you like.