The Brandybuck Family began as the Oldbuck clan, who named themselves such apparently after a Bucca of the Marish, who became the first Thain of the Shire. Ten Oldbuck Thains followed, until Gordenhad Oldbuck, the twelveth Thain, crossed into Buckland over the river Brandywine.
The Brandybucks formed a powerful dynasty which became mostly independent of the Shire, although Buckland remained nominally a part of it. They were seen as 'odd folk' by the other Hobbits of the Shire because they locked their doors at night (because of the exposure to the Old Forest).
The head of the family was the Master of Buckland, one of the officials of the Shire. This office was founded by Gorhendad Brandybuck. It was traditional for each of the Masters to have an epigraph attached to their names, such as Gorbadoc "Broadbelt", Saradoc "Scattergold", and the most famous, Meriadoc Brandybuck the Magnificent. Like the Thain and Warden of Westmarch, the Master had only nominal authority.
Brandybuck Family Tree
Brandybuck of Buckland.
Brandybuck is a rare English name which I Tolkien had come across.