The forest behind Hogwarts is home to a large population of centaurs, which are a nod to classical Greek mythology. In early Greek myths, centaurs are creatures that are half-man, half-horse, and are often lustful and boisterous- with the exception of Chiron, a centaur wildly known for his wisdom and his role in training several Greek heroes, including Achilles.
Professor Trelawney can also be seen as an allusion to Cassandra, a prophetess from Greek mythology, who was cursed to tell prophecies that were true but that no one would ever believe. Trelawney is faced with a similar plight; most of her prophecies are the product of hysteria and are complete nonsense, but she did foretell the great prophecy foretelling Voldemort’s defeat that is introduced at the end of this novel. While this prophecy came true, resulting in Harry and his ability to defeat Voldemort, her reputation of telling false prophecies left many people reluctant to believe her. Trelawney’s first name is also Sybil, which was the name for the high priestess of Apollo in Greek mythology.
Remus Lupin’s name refers to Remus, the mythological founder of Rome who was supposedly raised by wolves, and the word lupine, which means “to have wolf-like characteristics.” Both allude to his being a werewolf.
Sirius Black’s name is a reference to Sirius, the dog of the hero Orion in Greek mythology. Sirius’ animagus takes the form of a dog.
Hermione’s name is a reference to the only child of Menelaus and Helen, also from classic Greek mythology.
Harry himself can be seen, in many ways, as an allusion to the legendary King Arthur- a young man, orphaned as a child, who has been prophesized to vanquish evil from his world and restore order, with a supportive and close-knit army at his side. (In Arthur’s case, the Knights of the Round Table, in Harry’s case, the Order of the Phoenix and Dumbledore’s Army.)