Dumbledore's full name is Albus Percival Wulfric Brian Dumbledore, as he states during the fifth instalment in the series, Harry Potter and the Order of the Phoenix. The name "Dumbledore" is an old Devon word for "bumblebee" and was picked by Rowling because she imagines him wandering around the castle humming to himself.
The name Albus is the Latin word for 'white', a frequently used symbol for good, which marks the character out as an enemy of the 'Dark Lord'.[8]
Percival is a name from old French, meaning "pierce the veil".[9] It was the name of one of King Arthur's knights. While Galahad was the only knight pure enough to be permitted to hold the Grail, Percival was permitted to see it. The oldest recorded version of Percival's story is Chrtien de Troyes' Conte du Graal, from the 12th century. In Alfred, Lord Tennyson's "The Holy Grail", one of the Idylls of the King,
Percival is both hero and narrator of the tale, as is the case for Dumbledore in parts of the Harry Potter books.[10] And as revealed in Harry Potter and the Deathly Hallows, this is also his father's name.
The name Wulfric means "wolf-power" and is reminiscent of the legendary hero Beowulf ("bee-wolf"; a kenning for "bear"), who, in his early years, slew the monster Grendel (a name oddly similar to Grindelwald, a Dark Wizard whom Dumbledore defeated).
The name Brian is of Celtic origin and its meaning may be "hill" or "strong, noble, and high". Brian means a matter strength, dignity, and honor. Another meaning for this name is "majestic and powerful in Irish rule." It could also come from the ancient British word for "king" (*brigantinos, Brythonic *brijanin, Welsh brenin). Also, Brian is the only of his otherwise unusual names which is still used fairly commonly today- this shows a somewhat comical and eccentric edge even to his name, which certainly fits Dumbledore's personality.
It has also been noted that the name 'Albus' bears a resemblance to the name of a 19th-20th century stage magician, 'The Great Albini', who was a friend and rival of the less proficient magician Horace Goldin (who is described as similar in appearance and nature to Horace Slughorn).
In short, Dumbledore name suggests his personality.