Albus Percival Wulfric Brian Dumbledore is it, as we learned from the headmaster's Wizard Card from the Chocolate Frogs on the Hogwarts Express in HP and the Philosopher's Stone.
Albus comes from the Latin word for white, as well as suggesting Albion, an ancient, Arthurian name for Britain.
Percival was one of the King Arthur's knights who attained the Holy Grail. He shares this name with Percy Weasley.
Wulfric has a most interesting possible source. Grindelwald looks much like the monster Grendel in the 8th-century Norse epic Beowulf and Grendel. If you break down the names, Beowulf breaks down to BEO = 'powerful bear' and WULF = 'wolf.' Dumbledore's second middle name breaks down to WULF = 'wolf' and RIC = 'power, rule.' Considering Dumbledore conquers over Grindelwald in 1945, I would say there is a high probability Dumbledore's second middle name is an allusion to THE Beowulf and Grindelwald's name is an allusion to THE Grendel.
Brian (not addressed in source) has an uncertain meaning but it is possibly related to the Old Celtic element bre meaning "hill", or by extension "high, noble". Brian Boru was an Irish king who thwarted Viking attempts to conquer Ireland in the 11th century. He was victorious in the Battle of Clontarf, but he himself was slain.
Dumbledore is an old English word for bumblebee, according to JKR, who says that she imagines him wandering around the castle humming to himself. Interestingly, the word "dumbledore" has another possibly important meaning. Although not widely known, an alternate meaning for the word Dumbledore is a style of hat the was made semi-popular in London in the 1880s-1890s. Taking this meaning into account, Albus Dumbledore's name would have the meaning "White Hat." As I'm sure you know that is a term for the hero or protagonist of a story. Mrs. Rowling named her great champion of good "White Hat."
http://www.hp-lexicon.org/wizards/dumbledore.html#Name
