Fluffy the Three-Headed Dog
Based on Cerberus in Greek mythology. Three-headed dog who guards the entrance to the underworld/realm of the dead. Lulled to sleep by Orpheus, who played music for it. Getting past Fluffy a symbolic death? Hagrid: "Bought him off a Greek chappie..."
The Basilisk
Greek basiliskos = "little king". In Greek mythology and medieval folklore: King of the serpent, can kill with a single glance. The basilisk in ancient Greek texts: small, but deadly serpent. Pliny the Elder (1st cent. CE): Basilisks can only be killed by weasels.
The Phoenix
Greeks: Identified benu bird with phoenix (Greek: Phoenician), crimson color.
Zeus
Symbol is a lightning bolt.
Alecto
One of the three Erinyes (goddesses of vengeance) in Greek mythology. Alecto (Greek): "the implacable". Cp. the female death eater Alecto Carrow in Harry Potter 7.
Amycus
A Trojan warrior in Greek mythology. Known for his boxing skills. In Harry Potter 7: Alecto's brother, death eater.
Perseus
Has invisibly cloak. Son of Zeus. Prophecy about the baby: Will kill evil king (cp. prophecy about Harry and Voldemort) Kills Medusa, monster who turns people to stone by looking at them (cp. basilisk). Looks only at her reflection in a polished shield. God Hermes gives him magical sword for the task: Slays sea serpent and rescues maiden (Andromeda). In later legends: Perseus also tames and rides the winged horse Pegasus (cp. Buckbeak).
Hermes
In Harry Potter books: Percy Weasley's owl. Named after Greek messenger god. Precocious infant, steals the cattle of the sun god Apollo. Carried a staff/wand Could use it to cast spells so people would fall asleep.
Hestia
In the Order Of The Phoenix. Laughs at Aunt Petunia's potato peeler. Hestia: the Greek goddess of the hearth and domesticity
Merope
In Greek mythology: Immortal woman married a mortal man and was punished for it. HP 6: Merope Gaunt (Voldemort's mother) punished for marrying a Muggle.
The Black Family
Named after stars - and stars after Greek mythological characters (Alphard, Andromeda, Pollux, Cygnus, Regulus, Arcturus, Phineas, Cassiopeia, Narcissa, Lycoris, Lysandra.)
Centaurs
In Greek mythology: Centaurs are half men, half horses. Wise Teachers to many famous Greek heroes, like Achilles and Hercules. Dumbledore hires a centaur to teach at Hogwarts (OP)
Unicorns
Described in Greek works on natural history: Real animals, live in India.
Hippocampus
Mythical animal. Pulls the chariot of the sea god Poseidon. Mentioned in Magical Beasts and Where to Find Them.
The labyrinth
The Labyrinth of Crete: Minotaur (monster) in the middle. Cp. maze in the Goblet of Fire
The Nimbus
Greek gods often depicted with a nimbus, a shining cloud (halo). Cp. broomstick Nimbus 2000
The Ring of Gyges
Described in Plato's Republic. Magical ring that renders the wearer invisible. Gyges uses it to seduce a queen, kill her husband, and become king.
Ancient Greek Magic
Polyjuice potion: Similar to the potion used by Circe to transform men into pigs in the Odyssey? Used a Wand. Asphodel: Eaten by the dead in the Greek underworld. . . "For your information, Potter, asphodel and wormwood make a sleeping potion so powerful it is known as the Draught of Living Death..."
The Sphinx
The sphinx asks Oedipus a riddle in the play Oedipus Rex. The sphinx asks Harry Potter a riddle in Goblet of Fire. Originated in Egyptian mythology, but popular among the Greeks
Holly
Ancient Greeks: Holly protects against magic and poisons.
The founders of Rome
Twin babies Remus and Romulus, sons of the war god Mars and the priestess Rhea Silvia. Their grandfather's brother tried to kill them, left them in the wilderness. Some versions: Servant put them in a basket and put it on the river. Babies nursed by a wolf and lived in the wilderness. Found by a shepherd who raised them. Later, Romulus killed Remus. Romulus became the founder of Rome. Cp. Harry Potter character Remus Lupin.
Luna
The goddess of the moon. Cp. Harry Potter character Luna Lovegood
Minerva
Roman goddess of wisdom, corresponds to the Greek Athena. Athena/Minerva can change people's appearance. Minerva McGonagall teaches transfiguration
Aurora Sinistra
Aurora: Roman goddess of the dawn. Sinistra: "left hand", but also the name of a star. Aurora Sinistra: Astronomy teacher at Hogwarts.
Ancient Roman Magic
Witches often associated with theft of body parts from the dead - look for this in later books.