A genealogist from Nova Scotia who takes live phone-in calls once a month on CBC Radio in Halifax was asked about the name BUCKMAN on the July show phone-in last week.
He said that BUCKMAN and BUCKNAM could be different forms of the same surname, and that the name might have come from BUCKENHAM or BUCKINGHAM in the Norfolk-East Anglia area of England, north of London (the port of Great Yarmouth is nearby).
As you likely know, "-ham" on the end of an English word meant "settlement" or maybe "village". "bucken" sounds like it might have German or Dutch roots from long ago, but that is only my thought. My feeling is that it is not connected to the Normans and William the Conqueror of 1066. I think these people were already livling in England when the invaders landed.
The name BENEY is interesting. There are very few across Canada, and all the ones in NB are between Saint John and the Maine border. It sounds like it was French a long time ago (Benet ?). Was it maybe Huguenot ?
Searches through the phone listings can be interesting - I notice that the only BUCKMAN spellings in NS where I live are all at the tip end of Long Island in Digby County - right across the Bay of Fundy from where you are !