So Elizabeth Marguerite arrived August 15th. We call her Eliza. New question: when you have a child that has a given name but you call them by a nickname how do you introduce them to people, by given name or nick name? This is something new for me.
I think it depends on the age of the child, on who's doing the asking, and on how pervasive you want the nickname to be.
When a baby is first born, I think everyone wants to know the full name, and so I'd say to all the people in your lives (relatives, friends, co-workers, fellow club members, acquaintances, nurses at the hospital), "Her name is Elizabeth Marguerite. We're calling her Eliza."
For strangers who coo over her in the store and ask what the little sweetie-biscuit's name is, I think you could say "Elizabeth" or "Eliza"---or, if the stranger were Swistle or seemed otherwise especially interested, you could say "Elizabeth, and we're calling her Eliza."
Once she's older, I think a good rule of thumb would be to introduce her as you'd like her to be called by the people you're introducing her to. If you want everyone to call her Eliza, say her name is Eliza. If you want people to call her either Elizabeth or Eliza, whichever they'd prefer (but not to launch off into Liz and Beth and Libby), I'd introduce her as "Elizabeth---or Eliza, for short." If a little kid at the park asks what her name is, say whichever name you think the little kid should call her. At the doctor's office or school office, you'll refer to her as Elizabeth, because that's what they'll have on the paperwork, but when you meet the actual doctor or actual teacher, go with "This is Elizabeth; we call her Eliza" or "This is Elizabeth---or Eliza, for short," depending on if you want the call-her-Eliza-please option or the call-her-Elizabeth-or-Eliza options.
As she gets older, she may help you by expressing her own preference. If you've called her Eliza all along, she'll probably introduce herself that way, and you can teach her to say politely things such as "Oh, yes, my full name is Elizabeth, but I mostly go by Eliza."
More ideas for introducing a child with a nickname?