The surname most likely derives from the town of the same name on the Isle of Wight: Brading. The entry for this in the Oxford Names Companion states:
Brerdinges 683, Berardinz 1086
"(settlement of) the dwellers on the hill-side"
Old English brerd + -ingas
Brayding - Bradinge - Braydinge
These are my Brading ancestors in alphabetical order (the hyperlinks will take you to my tree elsewhere online):
As you can see they didn't have a very original line in Christian names! I have a WikiTree showing just my direct line down from John.
My Bradings in History
Most of my Brading ancestors were masons and lived in Shorwell until the late 18th century when they had moved to Ryde. George Brading (1818-c1880) was the first butcher and tradition which passed down until my great, great uncle George Brading who owned the butchers in Brading itself until the 1960s.
My great, great uncle Alex (Alexander Thomas Brading 1877-1962) fought at the Battle of Omdurman under General Kitchener. Another lancer at this battle was Winston Churchill.
This is my first post for http://www.geneabloggers.com/ Surname Saturday.