Again, it's a Smith and Wesson "Hand Ejector". That's it's name. It is a 2nd Model large (or .44) frame due to the lack of the barrel shroud (the visible clue) and the lack of the crane lock. It was originally in .455, hence it was called a ".455 Hand Ejector" to be caliber specific. S&W would have likely called it a "First change" for internal purposes, but collectors call it a ".455 Hand Ejector 2nd Model".
It was converted to .45 Colt ("Long Colt", to some) after it left military service, so it's not "pristine".
ETA: I've only ever heard the "New Century" designation in reference to the previous model, i.e., the "triple lock" or "1st Model".