Cobham = "old round farmhouse" (very old name)
Once a month on CBC public radio in Nova Scotia there is a phone-in show on genealogy. Recently this name was brought up, and the guest host Terry Punch said Cobham is a very old name with Anglo-Saxon roots (before William the Conqueror in 1066).
"Cob" has the meaning of a "round building" and "-ham" on the end of a surname indicates farm land. So Cobham means "a round building on a farm" - whether it was a barn or the farmer's home is not clear.