The official name is "COMBINED RACING GREYHOUND HARNESS AND RIDER SUPPORTING MEANS," but I like mine better.

From the application, filed in 1932:

In the sport of greyhound racing, that is enjoyed by dog fanciers and racing enthusiasts, there has been recently introduced the use of monkey riders, who serve in the capacity of jockeys…. The employment of the monkey jockey adds considerable zest and enjoyment to the sport. However, as in horse racing, there is ever present the danger of the rider being accidentally thrown…. To, therefore, provide a safe, humane, unique and most efficient means for retaining the monkey rider on the greyhound to assure against accidental displacement of the jockey…, I have devised the present combined harness and rider support.

Note that the little monkey jockey hat is not among the claims made in the patent. The little monkey jockey pants are.