In most Thoroughbred racing jurisdictions the owners line is limited to around 3 names due to space constraints. At least that what I was always told. It will list the allowed number of names given by the syndicate manager with an “et el” after.
With my racing partnerships the partnership agreement states how the owners line will be dealt with. It is based on the percentage owned. The people with the greatest percentage are first in order. How ever our stable name is always listed first regardless of our percentage by and large. But we usually own the biggest percentage anyway. If there are a number of small “fractional interest” owned then we choice a partnership stable name to go after ours.
My wife just got back from Luhmuhlen and her parents are in the syndicate that owns the horse that finished third. Without going into details it is a multi person syndicate all owning equal shares. I would suspect that as with a racing program there might be space constraints and it would not be possible to list say 10 different names.
My in-laws are 50% owners of another nice horse and their name is listed with their partner. As it should be IMO.
Regardless of the discipline owners IMO are the MOST important part of the equation. And should be given the most “press” and attention. Regardless of discipline most horses end up being “also ran” types. So making the experience a prideful and fun one is imperative.