Do you mean like a prefix or suffix or initials in a horse's registered name?
Unless Canada has some specific "national" rules regarding registering farm prefixes/suffixes/initials/names etc., it would be up to the breed organization with which you register how they handle it. Some registries allow for reservation of a prefix (etc) for a particular farm/breeder only. Other registries do not-- anyone can use whatever legal allowable name, as long as it is not already taken-- "first come first serve". (although most breeders avoid using a name that would confuse their horses with any other farms'/breeders' produce-- they want something unique and identifiable.)
I can't find anything regarding registering/reserving a farm name with RPSI. Your best bet would be to contact them directly and ask. I did find an archived discussion which might be interesting-- seems like reserved prefixes are more common in some pony breeds, and that the changing or replacing/dropping of prefixes is a concern. Usurping a Prefix [Archive] - Chronicle Forums