Actual names cited by the lawyer for the Georgia Department of Health in a letter to the ACLU explaining that there is some power of the state to reject names that parents might want to impose on their babies. But the lawyer was also denying that the last name "Allah" was rejected because there was something substantively wrong with the name. The state says the problem is only that the last name on a birth certificate from the Office of Vital Records needs to be either the mother's last name, the father's last name, or some combination of the 2. If you want some other name, you should petition the court for a name change, and any problems with the name will be addressed at that point.
Here's the report in the NYT, which seems to be saying that the ACLU's argument is only based on a provision of the state statutory code that says birth certificates need a name "as designated by both parents." I'd like a link to the whole statutory provision. I guess the fight is over whether parents get to choose a last name as well as a first name at the birth certificate stage. An ACLU lawyer is quoted saying the parents "feel very strongly that they want all of their children to have the same last name." The parents — whose last names are Handy and Walk — already have 2 children with the last name Allah. (One of them is named Masterful Allah.)
Remember when Paul Kantner and Grace Slick named their baby God? False! Grace Slick just said the baby's name was "god" — "We spell it with a small g because we want her to be humble" — but that was just some fluffy blah blah of the time. The baby's name was China.