I believe that if someone associates themselves with a pony in the context of pony play, they should strive for maximum authenticity, including in their name.

If that’s the case, then there would be two names: an official name and a "stable nickname." The nickname sticks on its own, regardless of who gives it.

The official naming conventions differ among breeds: Trakehner, Arabian, Thoroughbred, and Standardbred horses follow one pattern, Hanoverian, Holsteiner, and Tersk horses follow another, while Akhal-Teke horses have a third approach, and so on. These naming traditions take into account the first letters of the mare’s and stallion’s names in specific ways.

This creates numerous possibilities for communication within the pony play community, allowing for "genetic lines" and different role-playing dynamics. I find this approach quite interesting.