so the name "Gwangjong" (and also his father's name Taejo) is called a "temple name." Temple names are names that historians give to Korean, Chinese, and Vietnamese royalty after their death. They're made up of two characters: an adjective that describes their reign, and either "jo" or "jong."

"Jo" means "forefather," and was used to indicate one who founded a dynasty (ex: Wang So's father was given the name Taejo, because he founded the Goryeo dynasty).

"Jong" means "ancestor," and was used for the other rulers in that dynasty (this changed after Goryeo became a Yuan state under Kublai Khan. He felt that naming Goryeo royalty like that weakened his own power, so he kind of demoted them from emperors to kings, which is reflected in the temple names of close to a dozen rulers until the next Taejo [of the Joseon dynasty]).

As for the adjectives... some were praiseworthy, and some were more deprecating. Some rulers of Goryeo:

Taejo (太祖; Great + founder)
--太, meaning great or grand, was often given to founders
Hyejong (惠宗; Compassionate + ancestor)
--惠 was given to those who treated the people compassionately with a gentle quality
Mokjong (穆宗; Majestic + ancestor)
--穆 was given to those who preached their virtue and righteousness to the people
Munjong (文宗; Civil + ancestor)
--文 was given to those who sympathized with people and recognized their needs; along with 武(Mu) this is considered a very honorable name
Gwangjeong (光宗; Bright/Brilliant + ancestor)
--光 Gwang as a noun is "light," but as an adjective means "bright"

this is really verbose. tl;dr version:
"Gwang" isn't specific to a certain era... It's just an adjective, and it's still used in names today (for example, Lee Gwangsoo, from Running Man uses that same "Gwang" character). It was given to Gwangjong after he died to indicate something about his rule.... I honestly can't tell you what that something is, though, because Gwang seems like a positive adjective to me, but from what I remember of my Korean history classes during his rule he squashed his political rivals. He killed people before they could revolt against him.... buuuut I also read that he had public support because he supported Buddhism so maybe he was nicer to his people than he was to his opponents, idk (ok so this isn't REALLY a tl;dr version of anything sorry i talk alot)

Her name in Korean is Lee Ha-nui, and I assume that they translated it as Honey to make it easier to say.
I think that was during the Miss Universe days though...although I'm thinking they just stuck with that English-ification of her name in her post-Miss Korea career.

I hear you my friend...slipped into a dream world right after, didn't you? Forgetting this was about Lee Honey and NOT you.