Final answer:
Luna Lovegood wears a Lion's Mane Hat to support the Gryffindor Quidditch team during Harry Potter's sixth year, distinct from ancient cultural headdresses.
Step-by-step explanation:
The type of headdress Luna Lovegood wears to support the Gryffindor Quidditch team during Harry's sixth year is known as a Lion's Mane Hat. This information is from the "Harry Potter" book series, where Luna is described as showing support by wearing a hat that resembles a lion's head, complete with a roaring sound effect. The hat is to show her support for the Gryffindor house, which has a lion as its emblem. Despite the various headdresses worn by deities and figures in ancient cultures, like the Syrian goddess Kybele, Luna's choice of headwear is purely for the support of her friends and has no connection to shamanic traditions or symbols of power.