The most famous example of not naming babies on the spot would be the Street family of Idaho. Picabo, I believe, chose her own name (and screwy spelling) aroung age five; I remember that she had a brother who was allowed that same privilege.
This is in fact one of Cecil’s columns, not a Mailbag item: Is it illegal to take a newborn home from the hospital without naming it first?
We have two different forums, one for responses to Cecil’s columns and one to responses to the Mailbag items (written by the Straight Dope Science Advisory Staff, watched over by Ed Zotti, but Cecil himself doesn’t play a role with the Mailbag – there’s no money in it.)
Since this question is related to a column, I am moving it to the forum “Comments on Cecil’s Columns.”