I agree with Kingsblade. If we had a cup, we could call it the Naismith Cup, just like the Stanley Cup. However, we call it the NHL and not the Stanley Hockey League.
Of course, until the NHL felt it had to appeal to the lowest common denominator, it had conferences called Campbell and Prince of Wales, and divisions called Patrick, Norris, Adams, and Smythe. All in recognition of the history of the game.