Horse's name
A window with one field: the horse's name, twenty characters at most. Next to it, a button that draws one at random — handy when inspiration is lacking, and for christening a batch of foals quickly.
Names drawn at random are often English
It is not a setting you have missed: the generator draws an English name seven times out of ten, and the rest of the time a name in your language — French or Spanish. You will therefore get English names most of the time, even playing in another language. That fits the racing world, where English names are at home.
Languages are not built the same way: in French and Spanish a noun followed by an agreeing adjective, in English an adjective followed by a noun. If the suggestion does not appeal to you, draw another one — or ignore the button and write what you like, the field is entirely free.
The name is unique within your breeding operation, not in the game
It is the only rule to remember, and it surprises in both directions. You cannot have two “Tornado”s in the same breeding operation; on the other hand another breeder can perfectly well have his own, and several “Tornado”s therefore coexist in the game without getting in each other's way.
The breeding suffix is what tells them apart, and it is what defines that name space. See breeding.
Practical consequence: if the game refuses a name saying it is not unique, it is because you have already used it — including on a horse you have sold since, as it remains attached to your breeding operation.
Renaming is free
No cost, no delay, as many times as you like. A horse is not bound to the name it received at birth, and renaming has no effect on its results, its medals or its pedigree: it is a label.
Two remarks all the same. The name is what other players see in the runners and in the rankings, so it represents you. And a horse for sale that is renamed throws off the buyer who had spotted it.
Who can do it
The owner. The trainer and the jockey, no: they work the horse, they do not christen it. For a clan horse, it is the clan's owner.
To name a horse when creating it, see Create a horse; the same automatic generation is offered there.
