And if you ask me, they should both be charged under truth in advertising statutes.
Who are they? Why the Naked Cowboy and the Naked Cowgirl of course!
It seems from what I can tell that the Naked Cowboy has been performing this character since 1997 and in 2001 he moved to NY (the same time moved to go to law school, and he and I are the same age - how different our choices have been) and started performing in Times Square.*
The Naked Cowgirl was a stripper for years but in 2008 she started dressing in her underwear and singing and playing guitar in Times Square.
He sent her a cease and desist letter.
Then he sent her a franchise agreement (Yes, you too can be a Naked Cowboy if you buy a franchise)
When she continued her performances and never signed an agreement, he finally filed suit against her, alleging trademark infringement and other unfair trade practices.
This is not the Naked Cowboy's first rodeo.
In 2008 the Naked Cowboy sued the M&M Mars corporation, claiming $6million for violating his trademark. The candy company had made a commercial specifically to broadcast in Times Square, showing a blue M&M with cowboy hat, cowboy boots and briefs, playing guitar and singing. That case settled.
This is not a multi-million dollar case, and I can't predict whether or not it will settle, but the outcome is not as easy as you might think. First off there's no copyright protection in the character because it's not written down but performed. Second, trademark protection is not settled on the issue of characters. Some courts will find it but others will require the character be attached to a product. That could make the evidentiary stage of the case rather difficult for the cowboy. That leaves unfair practices, and that's an animal of state law. New York has a thriving art scene of course, so I suspect that there's good precedent for protecting performance art against immitators.
In any case it's an interesting case to watch (though looking at the pictures above, maybe "watch" isn't something I want to do).
*and for just $499 you can get married by Reverend Naked Cowboy in Times Square!