How would you make that case? There are plenty of restrictions on free speech as well as freedom of the press, which is far from absolute, and is most certainly regulated.
True, but a restriction on printing the names of criminals and victims would be considered a "content-based restriction," which are subject to strict scrutiny.
There is an established legal basis for allowing publication of victim's names: "Thus, it is ordinarily unconstitutional for a state to proscribe a newspaper from publishing the name of a rape victim, lawfully obtained. This is because there ordinarily is no compelling governmental interest in protecting a rape victim’s privacy" (4). IANAL, but permission to print criminal's names (which are obtained legally) follows from similar logic.
"Ordinarily" also implies that it's subject to change. There's nothing inherent in the law that prevents the change being discussed, other than the status quo.
There is an established legal basis for allowing publication of victim's names: "Thus, it is ordinarily unconstitutional for a state to proscribe a newspaper from publishing the name of a rape victim, lawfully obtained. This is because there ordinarily is no compelling governmental interest in protecting a rape victim’s privacy" (4). IANAL, but permission to print criminal's names (which are obtained legally) follows from similar logic.
[0]: Congressional Research Service: Exceptions to the First Amendment: http://www.fas.org/sgp/crs/misc/95-815.pdf