I understand both sides. If you go through all the expense and trouble to hardship, and want to use your own farm name... but then again, you weren't the breeder. I guess it's a personal choice what to do.
In my own experience... 29 years ago we bought our stallion, Jet as a foal, we also bought his half sister. The breeder sold them both on application and we put our farm name on them both. At the time i felt that if i am paying to register them, i might as well put my own farm name on them.
But over the years, i kind of wish i hadn't. I probably should have left a pre fix off altogether.
So, now 2 years ago, I bought another stallion. He was only AMHA reg. So I hardshipped him into AMHR.. I just dropped the farm prefix, and kept the rest of his name. I just feel better about doing it this way.