I think it's fine to change barn names, but I don't necessarily agree with changing the registered name, (especially if you show) unless you notify the breeder of the horse that you're changing it. I was reading about this on another forum, and a lot of the breeders were upset about registered names being changed, not because of personal reasons, but because it was much harder to keep track of their horses offspring in the show ring. They of course want to pay attention to their accomplishments.
I never even thought about it that way until looking at it from their point of view. Another thing they brought up was that maybe if you do end up changing the name, you can keep the farm initials in the name so people are still aware that they come from that facility. Of course that wouldn't apply to horses without any initials but I think it makes sense for horses that do. (For instance, your horse is named RTA Joe Schmoe-RTA standing for Red Tail Arabians. So you want to change his name to Spitfire, you would instead make it RTA Spitfire.)
Just another way to look at it :)