Each sport has different conventions, which, if you want to fit in, you must adhere to.
Thoroughbreds have a rather small number of allowed letters and spaces, one of the oldest registries (late 18th century), and the rule that no foal can have a registered name that duplicates another name in the registry. Since all horses have to be registered to race, thousands of foals are registered each year, so a main reason TB names seem kind of random is because they can’t be a duplicate.
There are really no naming conventions in that world, unlike in other horse registries, which are more like the dog registries in that certain ways of naming are “right” and all others just plain wrong.
Horses rarely know their names, as it is not necessary for handling them – you use lead ropes and reins, whips, heels, and shifts of weight to communicate with them, not words. “Stable” names are for convenience and they often change as the horse changes hands.
Show dog naming arose from a different tradition. Originally, dog shows were a Victorian fad of the upper classes, which had estates to raise them on, so they tended to be named (Dog Name) of (Name of Estate), a convention which came out of rural livestock fairs in which Crumpet of Greymead Abbey retires the West Snicket Champion Milch Cow trophy.
When dog showing became a middle class suburban hobby, its naming conventions went with it, hence a show dog will have the official name of its breeder’s kennel (although the ‘kennel’ is not a place, just a name invented by the breeder), plus its own “show name” as its whole registered name. They invariably also have a “call name” which just an ordinary dog name.
Champion Fantastic Four of LuvsAFuzzy Acres, aka Spud, probably lives in a suburban backyard along with ten other neighbor-annoying relatives. The majority of registered names are taken from popular culture, or very conventional romantic tropes like Windswept, Golden Sun, etc. Often they are cutesy puns, and often they refer to one or other of the parents. Maybe not all at the same time.
The Dog Fancy ladies (they are virtually all women) love being able to name a dog a long stupid name and have it printed on an official certificate.They spend a lot of time and thought on it, and it is a big part of the hobby.
It is a strange little world. But every hobby is strange from the outside.
There. Sorry you even asked?