Are there laws that prevent media outlets (radio, Television) from
identifying Juvenlies by name in stories and articles? Say if a woman
was arrested for abusing her son, 4 years old. Could a News station
say the child's name, legally? Also, do these laws vary by state? is
there somewhere I can find what states have what laws?

"In the unanimous 1979 decision, Smith v. Daily Mail, 443 U.S. 97
(1979), the U.S. Supreme Court ruled that the First Amendment protects
the right of journalists to use the names of minors in newsworthy
stories as long as the information is "lawfully obtained" and
"truthfully" reported."

From http://www.splc.org/legalresearch.asp?id=29

My understanding is that law enforcment generally cannot release this
information without the consent of the legal guardian.  However, if
the news outlet receives the name from another source, then they are
free to print it.  Also, once the minor's name is stated in an open
court, it becomes a matter of public record.

The media generally doesn't report the names of minors for ethical
reasons, but I don't believe they are legally forbidden to do so.