You can attach any identity you want to a TBs microchip, for show purposes (not for racing).
The way it goes: the horse is doing bigger things and needs a USEF or FEI passport. The vet scans the horse to see if it already has a chip. Oh, yay, it does! One less thing to do. You record that number on the passport and whatever show name the owner gives you. Boom, that horse has whatever show identity you want, attached the microchip it already has. No one cares. USEF and the FEI don’t cross reference microchips to every breed registry.
Also, more common than you might think to have more than one microchip in a horse. Some (older) horses had the old style microchips implanted and had to have a newer one put in. Microchips migrate, and you can find the breed registry chip on first scan and they pop in a new one for show purposes, etc.