New Jersey Section 8:2-1.4
(a) The designation of a child's name including the surname is the right of the child's parent(s). The child may be given any chosen name(s) or surname, except that
the State Registrar may reject a name that contains an obscenity, numerals, symbols, or a combination of letters, numerals, or symbols, or a name that is illegible.
You'll be glad to hear that Alabama allows most anything (even obscenities like
Crimson Tide), so long as it doesn't contain "numbers, periods, symbols, or non-English alphabetic characters":
AL 420-7-1-.04 Name of Child for Registration of Birth
(1) The parent(s) may give a child any name they wish for registration of birth. The surname of the child does not have to be the surname of either parent.
(2) The name entered on the birth certificate shall contain only English alphabetic characters, hyphens, and apostrophes. Other characters including numbers, periods, symbols, or non-English alphabetic characters may not be used.
Looking at the code in Tennessee, it appears that the magistrate had to give Messiah his father's last name as a matter of law.