Doesn't have to be on a board. Regs state that the number must be permanently marked so that alteration or removal would be evident. They use the term "on the main beam", but that goes back to wooden ship times. We don't have main beams anymore. A popular place is on a board mounted on the forward cabin bulkhead over the vee berth, but that doesn't really meet the reg because somebody could replace the board with one with a different number. Alteration would not be evident. You can put it anywhere you want, hidden in the bilge or engine room, or on display in the cabin. It just needs to be permanent, like carved or engraved into a permanent part. Most people don't do that though.
On the commercial boats I run, they're welded into a steel frame in the engine room.