The first thought that jumped into my head is make sure you reserve your farm name with your secretary of state. At least a DBA. Someone else could come along and call their farm the same name otherwise and it sounds like their program!
We register horses we bred or own with our business name. It can certainly be done with my name but may not be as well known as my business name in the long run. So the proper recognition method for us is using the business.
Hyperion Stud, LLC.
Europe's Finest, Made in America WWW.HYPERIONSTUD.com
Standing Elite and Approved Stallions
USEF doesn't have any naming conventions, so you could use a prefix or suffix as you wish. Most of the European type WB breeding organizations require that you follow their naming conventions, and the use of a prefix may not be allowed in those cases.
Our ponies are named with our prefix (Lorelei), which is very common for Welsh Ponies. The WPCSA allows for breeders to register prefixes and only they can use them, but that certainly doesn't stop anyone from using the same prefix when they register a pony/horse elsewhere, or from people dropping the prefix when they are showing at non-Welsh shows (unfortunately).
As for what name we register the ponies under, it is our farm name, not my personal name (for similar reasons as Hyperion).