Just migrating this information that I verified over from reddit into Lemmy.

I didn’t like the names of the Royal White stallion and the Ganon horse that got migrated over from my BOTW save file into TOTK. I released both the royal white Zelda horse and the black Ganon horse (one at a time to test it and keep my save files in case it went wrong). The Ganon horse respawned south of Hateno/east of Lurelin, the Zelda horse spawned north of Skull lake above the cliffs. For the Zelda horse I double checked before releasing and it did NOT spawn until I released it.

So if you want to rename your horses, make a save file BEFORE you release them, release them one at a time, and then go to the correct locations to recapture them.