I don’t know much about this subject except that anything doesn’t go when it comes to naming racehorses. I read an article about the subject once. There is a registration organization that prevents duplicates and disallows vulgarities – although the article did mention about how an occasional scampish owner is able to slip a roundabout offcolor name past their radar. (I wonder if the same people work at the vanity license plate office; I read an article to the same effect about them once too.)
As stated, they will disallow names perceived to be in unacceptably bad taste as well as names which have already been used. And yes, some owners have made a game of trying to sneak a naughty name by the committee, much like people trying to sneak something by the DMV for a vanity plate.
You can’t use a offensive name, but it is possible to sneak one by. One example was “Cunning Stunt,” though I don’t know if that horse actually existed. I do remember a “Brett’s Best Bet,” which led to a spoonerization of the first word by the track announcer. The call went “Breast . . . Bet Bet.” The last two words were spat out quickly as it was obvious he knew what he just said.
Not really on track, but my sister used to do a lot of equestrian show jumping back in the day. You wouldn’t believe the number of people who show name (typically horses would have a real name and a show name) their horses something like “Wish I Was” or “If Only I Were” or some other varient.
“Now showing number 17: Wish I Was owned and ridden by Jill Smith.”