Every breeder has a goal of producing the very best of their line -- with that they can show the world they know something (a little something) about breeding and their foals do take on a more desireable fate. I was very fortunate when I began buying a herd to happen upon a fantastic stallion with NO farm prefix. So he was promoted and shown to great results. From him I have sons with my farm name, all producing well (when I let them breed, that is
). I have actually kept the last few fillies I bred as they carry my farm name and are very nice mares.
Back to breeding -- yes, I'd prefer to show those with my prefix but know that when you are assembling your herd it is almost impossible at first. The
best way to show your prefixed animals is to sell them
then it becomes more affordable! Think about it -- takes a lot of years to raise you foals to mature breeding age. Besides, for me, buying a mare in foal doesn't "count" as my breeding. Thus to raise those you have bred from own stock to maturity, then breed them for your own breeding, is 6-8 yrs.
Add another yr for a foal to appear, then for them to grow and show -- Yep, 10-12 years involved

OH!
You spend a lot to promote -- advertising, shows, etc -- and while you would like your own prefix, it makes sense to also show that you have quality livestock
no matter the prefix. These will be your breeding stock, right?
We assume and promote....breed best to best, etc.