There are cultures where, due to high infant mortality rates, children are not named until after their first birthday.
ETA: Link to column: Is it illegal to take a newborn home from the hospital without naming it first? - The Straight Dope
no
When my aunt had one of her kids (long time ago, some point in the 80’s) it took them a long time to come up with a name and they would not let them take the kid home until they did. Would’ve either been in Ohio or Indiana (forget which of her kids this was, which would determine the state). Might not have been a law but it was at least in place there somehow whether just hospital policy or whatever.
It’s definitely illegal if the kid isn’t yours.
If the family stories are correct, my older sister was taken home as “Baby Lastname” and was not named until several weeks later. (Parental dispute; she ended up with my dad’s rather odd choice.) I’ve heard of other “Baby Soandso” temporary names.
Sometimes it takes a little time to come up with a good first name. For example, a 66 year old driver at my company is named(first named real, last name pseudonym) “Boy Smith”.
Remember the hooker on “Starsky and Hutch” who was named Female (rhymes with tamale)? She said after [8] kids her mom just didn’t care any more.
My grandson was expected to be a granddaughter. The parents hadn’t figured out a name until after they got home from hospital. No one arrested them that I’m aware of.
That was more or less the case for my sister; being born the unexpected gender, my father refused to give up on the (somewhat unusual but 100% male) name he’d selected. It of course conditioned me; to this day I hesitate when meeting men with this name. It seems as odd to me as the many thousands of people who have found my sister’s use of it odd.
No, but I remember the “Family Ties” episode in which neighbor Skippy discovered that he was adopted, and insisted that everyone call him by the name that was on his birth certificate: Baby Boy Doe.
Not very useful information without knowing the jurisdiction. I think we’re all agreed it’s not illegal everywhere; the open question is whether it’s illegal anywhere.
Powers &8^]
If everyone from everywhere responds as I did, we’ll have our answer.
The OP, for the record, did not ask if it’s illegal anywhere, he or she only asked if it’s illegal.
It might be illegal in jurisdictions with strict naming laws, like Iceland.
There’s definite culture bias in the question. How many births worldwide take place in a hospital? Even here, not all births are in a hospital, so the question assumes something which isn’t proven.
With the genders reversed, that’s what happened to Gene Robinson, the future Episcopal Bishop of New Hampshire: Gene Robinson - Wikipedia
Your family will pressure you to name the baby far more than the hospital will. 
The “name lady” only calls ONCE a day.
There is, in fact, a Picabo Idaho, ZIP 83313. 
1 - my roommate in college was not named when he was born. his first name on his B.C. was “boy”
2- when my son was born some 24 years ago in Massachusetts, he got a SS card before leaving the hospital (don’t recall if it was “state law” or “hospital policy” or just a suggestion) - wouldn’t he have had to have a complete name ?
p.s.love your columns
There will be bureacratic pressure, and it will be nigh well unavoidable if you mean to file an honest tax return (e.g., list all dependents as asked on the form). All dependents of any age on a tax form have to be identified by Social Security number. And you can’t be issued a Social Security number without a legal name:
However, mind-blowingly, a birth certificate isn’t usually acceptable as proof of identity:
Now, I can see there might be some wiggle room: the birth cert can lack a real name (“Boy Humperdink”), and still be issued; but I doubt you’d be able to apply for the SSN at the same time if you explicitly refused to name the child. If you do, I suspect what will happen is that your legal name becomes (by default) Boy Lastname or Girl Lastname (whatever’s on the birth cert), and that’s what’ll be on the SS card. “If you don’t choose a name, one will be assigned to you.”
Bureaucracies hate being circumvented, and if you do anything out of line, you have no guarantees anything will work well for you.
One hospital spokeswoman told me that when she was born 30 years ago in a Catholic hospital in Connecticut, her mother planned to name her Paige with no middle name. But a nun, armed with the certainty that only nuns can have, informed mom that no child was allowed to leave the hospital without two names. Glancing around, the mother spotted a box of Kimberly-Clark tissues and decided on the spot to name her daughter Kimberly Paige. (The child was never called anything but Paige.) It seems doubtful that the now-defunct hospital actually had a two-name policy, but you can see Jenn’s “belief system” goes back a long way.
My mother has a similar story. My grandparents wanted her name to be Helen Gregory Welch [for the sake of privacy, only the Gregory part of the name is real], but the nurse would not put the middle name down on the birth certificate because “Gregory is a boy’s name.”
Mind you, this was only her middle name; she had an acceptably feminine first name.
It was probably just the hospital’s policy, or even the nurse’s own prejudice that prevented my grandparents using Gregory as a middle name. So Mom doesn’t have a middle name.