I know there are a lot of decriers of the HP series out there, but I am continually amazed (at least in the earlier books) at how many literary allusions Rowling is able to entertain. As I was explaining to a recent class about allusions, it typically doesn't hurt if you miss the reference to your overall understanding of a work, but if you do happen to catch it, it's kind of a wink you can share with the author, a sense of being "in the know."
In the last two days, I've come across two more that had previously "alluded" (HAR!) me. Sagetrieb brought up "Septimus" in Woolf's work. Isn't there a character named Septimus in HP?
Where else do you find allusions?
There are many historical, biblical, cultural and mythical allusions in Harry Potter. Some of them are blatant, like Umbrage (her name literally means both rude and shady). Others are slightly more clever, like naming Harry Potter (when Christ was a carpenter) and Voldemort (flight from death). Sirius is the name of the dog constellation, and Lupus means wolf.
The only Septimus I can think of is Septimus Weasley, father of Arthur Weasley. I'm not quite sure the significance of his name though his character is important as background information. Apparently he had married Cedrella Black (of the Black family - an aunt of Sirius?) Similar to Sirius, Cedrella was removed from the Black Family tree because she was seen as a traitor.
Many of the Rowling's characters' names are references, especially the names of characters that can only be seen on the family tree. One allusion that I can think of right now is the names of Draco and his son Scorpius. Both of those names are constellations. Also, Draco is a word for dragon.