His name comes from the word "sinister", meaning evil. But "sinestra" means left in Latin. People have always used the word sinister to describe lefties, because people were convinced that they were witches, devils and other things throughout history. He also uses his green lantern ring with his left hand.
It is unknown whether he is actually left handed, but people say that he punches more with his left hand than his right hand, so I reckon that he's a leftie.
Hellboy's right hand is a big stone artifect thing, so he uses his left hand to hold weapons.