Etym: According to Rowling, "If you were hagrid-- it's a dialect word-- you'd had a bad night. Hagrid is a big drinker-- he's had a lot of bad nights."
Hannah Abbott: Etym: From Hebrew for "He (God) has favored me". In the Bible, the mother of Samuel, and in the Talmud, a prophetess; her prayer exemplifies successful petitions to God.
Harry Potter: Etym: Stated by Rowling on numerous occasions to just be her favorite male name.
Head Boy: A seventh-year student chosen for leadership and scholastic abilities who shares the prefects' duties.
Head Girl: A seventh-year student chosen for leadership and scholastic abilities who shares the prefects' duties.
Hebridean Black: A type of dragon native to the British Isles.
Hedwig: Harry's owl, named after someone he read about in A History of Magic.
Etym: Stated by Rowling to be a medieval saint, which would be St. Hedwig of Andechs. Another possibility is the devout but not canonized medieval woman who was crowned "king" of Poland at the age of 9, strongly supported religion and scholarship, and caused the restoration of the university of Kraków, which became the Jagiellonian University. (Here's the English root page.)
Hengist of Woodcroft (PS ch. 6): Was featured on a Famous Witches and Wizards trading card. Might be an actual historical person, but I haven't found any info on him.
Herbology: A required course at Hogwarts, taught by Professor Sprout.
Hermione Granger: Etym: A derivative of Hermes. Used by Shakespeare in A Winter's Tale as the name of a queen falsely accused of adultery, who dies of the shock when the evidence in her favor is disregarded.
Higgs, Terence (PS ch. 12): The Seeker for the Slytherin Quidditch team in Harry's first year.
Etym: From the medieval given name Hicke, a form of Richard, whose etymology is uncertain; may be riic "ruler" + heard "hard".
History of Magic: A required course at Hogwarts, taught by Professor Binns.
Hogwarts: The school for young wizards in the British Isles, housed in a massive castle with 142 shifting staircases, living paintings, numerous ghosts, and pretty much everything else that would have made your school the least bit interesting.
Hogwarts Express: The train that runs from King's Cross to Hogwarts at the beginning of the school year, and back at the end.
Hogwarts, a History: One of the books Hermione read to get ready for the start of school.
holly: Shrubs and trees of the genus Ilex, reputed to have protective powers. Harry's wand probably was made with English holly (I. aquifolium).
Etym: Rowling has given her reason for using it as its association with life and also with the word holy. Unfortunately, the second part is folk etymology; the word holly goes back to an Indo-European stem meaning "to prick". (Hollyhock, on the other hand, evolved from holy hock.)
Hooch, Madam: The flying instructor at Hogwarts, and usually the referee for inter-house Quidditch games.
Etym: No etymology. There was a minor Dutch painter named Pieter de Hooch, or Hoogh, or Hooghe (1629-1684).
Hufflepuff, Helga: One of the four founders of Hogwarts.
Etym: See below.
Hufflepuff House: One of the four houses of Hogwarts, it emphasizes hard work, goodness, and self-sacrifice. The house of the saints. Badge: Or, a brock rampant reguardant, at best guess, anyway. House colors are supposed to be black and gold. The house ghost is the Fat Friar.
Etym: Invented; along the lines of "huff and puff".
Humberto: see The Great Humberto.