Pistol Transfer Between Family Members

My father bought me a pistol as a gift for my twenty-first birthday as a gift, where he made sure to stay within the law. I recently informed him I planned on conclealed carrying with it, which he does not like because he believes the pistol is within his name. I informed him that Washington does not have a gun registry, but he still believes there is no way a gun cannot be traced back to him. Is there anyway a gun can be traced back to him, and if so, is there anyway he would be liable if something was to go wrong with this said firearm?