We were talking about birthparent-given names, and I was trying to make a connection to something I'd heard about naming babies in China. It finally hit me, and I googled "milk name" and found this:
When a baby is first born parents often give him or her a ‘milk name’ or ‘little name,’ such as Little Treasure. The given name is then chosen somewhat later: in China, parents have a month before having to register the child. The parents may continue to use the nickname.
I also want to mention a book I also described in the comments: Three Names of Me by Mary Cummings, for the benefit of those who don't read comments!