For some reason, the game will not allow me to change maybe a dozen of my horse's names. I type the new name into the box, and it says that the name was changed successfully, but it is still the same as before. I have tried several different names for each horse and get the same thing every time. Any ideas on how to fix this?

Most likely the names are already in use :)

I've tried several names for each horse though, and am not getting the message that says the names are already in use. That's what makes me think that that isn't the case.

Links to horses?

The game will give you the success message but not actually change the name when the only change you make to the name is a capitalization.