Not the Headmaster of Hogwarts, though J K Rowling must surely have borrowed his name from the bee also called a sumbledore. And a nicely echoic word it is, which evokes the drowsy hum of bees on summer afternoons.
Its first part is one of a set of rhyming words from English of some centuries ago, the others being bumble (from a root meaning to drone or buzz) and humble (from an old Germanic word meaning to hum). All three have been used to form names for those furry, blundering, slow-moving bees that are so large you wonder how they get off the ground (bumblebee is now the usual term almost everywhere, humblebee was once common in Britain but is now much less so; dumbledore is the rarest).
To various extents all imitate the insect’s buzz; the final dore of dumbledore is an Old English word for any insect that flies with a loud humming noise. Charlotte M Yonge used our word in The Daisy Chain, published in 1875: “Those slopes of fresh turf, embroidered with every minute blossom of the moor — thyme, birdsfoot, eyebright, and dwarf purple thistle, buzzed and hummed over by busy, black-tailed, yellow-banded dumbledores”.
The image of Professor Albus Percival Wulfric Brian Dumbledore takes a knock when you discover that our word is linked with the archaic or dialect dummel, for someone who is stupid and slow (our dumb and the German dumm are cousins) and dumbledore has also appeared in dialect as a name for a blundering person (Thomas Hardy put it into the mouths of a couple of rustics in Under the Greenwood Tree). Moreover, it has sometimes been applied in English dialect to a far less pleasant insect, the cockchafer (also called the May bug), a considerable pest of crops; it’s a large beetle that flies very haphazardly with a loud buzzing sound.