If a child was abandoned and only knew her first name, how would she get a surname? Or a birthday? I’m hoping such a kid wouldn’t just get stuck with “Doe” as a last name…
Okay well logically, what if the child were an infant? They social worker/foster family/adoptive parent…whomever wouldn’t call it bBaby Doe…they’d make up a name. I think it is the same.
I had a neighbor once that was a foster mother for an adoption agency. She kept newborns while the adoption was finalized just in case the birth mother changed her mind, the new family wouldn’;t have to have the child and subsequently give it up. She gave each child a name, a baby book, took pictures, the whole nine yards even though she might only have them a week or two.
Her brilliant name scheme was to start with each letter of the alphabet. Her First child was Andrew Adams, then Briana Barnes…the adoptive family would then change the name to their own. But then it would be different for an older child who might keep the temporary name longer.
Still I assume some genius somewhere would give it a name.
It might be nice to name them after where they were found, like “Ernest Worthing” in The Importance of being Earnest.
Then again, “Dolores Doorstep” isn’t quite so pretty…
How about “Twist?”
My wife is a foundling, left on a doorstep in LA in 1948 (so it really does happen).
At the time there was no county adoption agency, so her case was handled by the probation department (I have no idea why). Someone there choose a name for her, choosing a Spanish name (Esperanza, which means “hope”) because she looked to be at least part latino. A court order then established her name and birthdate (based on an estimate of her age by a doctor).
Thanks for the “true life story,” Badge. This was what I suspected, but I couldn’t find any support for my theory on the local DSHS site. 
Bad-ass light-heavyweight boxer Matthew Saad Muhammad. Here is his story:
http://www.ibhof.com/saad.htm
During his career, however, it was said that he was given the name “Matthew” because that’s what the nuns thought he was saying when they asked him his name.
A friend of mine, back in high school, was in the foster care system her whole life. She was given her first name by the nurses within the first couple of days after her birth. Everyone along the way saw that she kept it. It wasn’t till a while later, maybe a month or two, that she was given the surname Smith. Whomever filled out the forms just snatched Smith out of the air, according to her first foster mom. We’re a smallish community so maybe we’re a bit more lackadaisical, not ready and organised like some might be, though.