It's like all the others have already said. But if you would breed a foal and would give him a name would you take one that is already taken 137419 times or would you give him a name that nobody has? And also you have high hopes in your foal and want it to become successful what if it has a pretty common name then? Nobody would remember your horse. But if there is a very very good "flying across the sky" horse, wouldnt you remember the name easier?
it's a registered or show name then they are called by their barn name. my mares registered name is Bar Money by Design and her barn name is Sierra. my other's show name is Ima Beach Bum and her barn name is Bailey