Fortunately the need to have surnames is now so well established that it is no longer necessary to invent them ~ except to use as "Stage" names and the like.
It all started with population growth and the need to differentiate between one person and another of the same name as in David that became firstly David son of David which soon contracted to Davidson and variations thereon (Davison etc).
Anyone called Cooper probably had an ancestor who made barrels. Thatcher is pretty obvious as well. Others were called after a local landmark or church within which boundaries the person had been born (as in the case of my ancestors) but it is no use looking at modern landmarks and trying to equate them as the name game started hundreds of years ago. Biblically it is starting to be used as in Joseph of Arimathea simply to show that he was not some other Joseph.