When it comes to GM vehicles, the paint code is NOT a name. The paint code is an actual code shown on the SPID (service parts ID) label and is usually numbers, but could be alpha/numerical at the very bottom and usually starting with "WA," but could also start with "L" or "U." That is the code that will determine the actual color and shade of the paint on the vehicle the label is attached too.
Any name given to any paint color on any GM vehicle is determined by marketing. The white used on H3s was marketed under the name BIRCH WHITE. It may have the same paint code as olympic white, arctic white, etc, I don't know. When ordering paint for any GM vehicle (and this is probably true for all manufacturers), order according to the PAINT CODE on the SPID (service parts ID) label. There could be a ton of whites, all with different names, with the same paid code; thus, they are the same color. And there could be a ton of whites, with different names and actual different shades of white.