At last, peace returned: the kingdoms of the Dúnedain fell one by one, and then the victorious Witch-king of Angmar was himself defeated by a revenging army of Gondor. The Hobbits returned to their old lives, but the loss of Arvedui, the last king of Arthedain, left them leaderless.
After four years had passed since the end of the great wars, the Hobbits decided to take a leader for themselves. They chose2 one Bucca of the Marish, who was granted the title Thain of the Shire, and led the Shire-hobbits to peace and prosperity.
No more is known of Bucca's life, but his legacy remained until the time of the War of the Ring and beyond. At that time, more than twelve hundred years after his Thainship, the Masters of Buckland still proudly claimed descent from Bucca the first Thain.
'Bucca' isn't a fictional name: it was fairly common among the Anglo-Saxons, with the same meaning as given above. (For example, modern Buckingham comes from Old English for 'Land of Bucca's People'.).
In the drafts of The Lord of the Rings Appendices, it is stated that Bucca was officially elected to his post, but this statement doesn't appear in the published work. (See The History of Middle-earth, volume 12, VIII The Tale of Years of the Third Age, 1976)