The fact that the farm is described in 1841 as "The Popyes Farm" doesn't mean that it wasn't also known at Breakspear Farm. Imagine a stranger visiting Bedmond at almost any time pointing to the farm and they might be told "The Pope's Farm" or "Breakspear Farm" almost at random. The stranger who knew nothing of the farm's history would find the first farm name more informative.Of course place names do change - but in documents such as the early census returns the address given may simple the way the census enumerator decided to record it. For instance in towns you may find a reference to "Jones Yard" in one census - if you look at the other nearby census returns you may find that at vthe entrance to the yard was a shop occupied by "Mr Jones".
In 1851 it may have been described in the census as "Breakspear Farm" but it could just as well have been called "The Pope's Farm" (Pope is easier to spell than Breakspear), "Mead Farm" (because the Mead family lived there) or "Edmonds Farm" (because the Edmond family used to live there).
In legal documents it might simply be identified by the name of the owner and/occupier - perhaps with the names of the people who owner/occupied adjuact plots. For instance in Land Tax records (available at HALS) there may be no farm name given, but it might be possible to identify it by the acreage!