The current U.S. National ruleset simply states that the king must be between 8 and 9cm on each face and 30cm tall with a weigh between 0.8 and 1.3kg. There is no mention of king design though "tournament legal" sets are all of similar design. As long as the surface area and weight of the king remains legal, it should be fine for competition.
However, in back-yard play, you can do whatever you want. We have a traveling trophy for the Des Moines Winter Klassic champion that is a king in the shape of the Stanley Cup. Granted, it isn't used in competition, but it is still a "king."