For CDE’s we have always needed our own number holders and we put them on our harness, and when driving pairs, always on the outside. When we enter a hazard on marathon day, I always yell out my number to the hazard judges just before we enter the gates so they can write it down on their sheets. For dressage, I have never yelled it out but we have gate people and they are aware on when to send us to the ring just before our test, so they know our number ahead of time We also have a number on the carriage but at speed, its hard to see (even with numbers on the outside ponies and one on the back of the carriage). But it has always been like this so I can see if some eventing shows have always offered numbers, and now they are not, its a change for sure!
We have purchased these number holders that would work on a bridle, halter or harness. Not sure if they would work for eventers? And here is a picture of it in use on our harness so you can see the size
https://www.drivingessentials.com/product_description.php?ID=51520");
When we show at Bromont CDE, they want a number displayed at all times, so even on a halter if you take them out of a stall. So they give us numbers that can easily be moved from halter, to bridle (for vet check) to harness. This way we are always identified. They also give a navigaor a pinny, but we have to wear vests over our farm shirts anyway, so I never mind wearing a pinny.