No, Barbaro means Barbarian in Portugese or Exceptional/Superior. They actually got the name from a foxhound in some painting they own. There is a great story out there about what Matz's assistant said Barbaro meant back in January.

http://tcm.bloodhorse.com/BarbaroSpotlight.asp

When trainer Michael Matz was asked if he knew where the name Barbaro came from, he called to his assistant, Peter Brette. “Hey, Peter, what does the name Barbaro mean?” he asked. Brette didn’t hesitate with his answer: “Kentucky Derby winner.”

“In our dreams, right?” Matz said.

But those dreams will become much closer to reality if Barbaro should handle the dirt in the Holy Bull Stakes (gr. III) Feb. 4 as well as he’s handled the grass. In his three career starts, all on grass, Barbaro has been untouchable, winning by a total margin of 201⁄4 lengths, including runaway victories in the Tropical Park Derby and Laurel Futurity (both gr. IIIT).