1.Generally in mythology, the Dragon is a symbol of Chaos, and therefore of Evil, whereas the gods are symbols of Law, the Order of creation, therefore of Good. Example: Tiamat and Apsu in Sumerian mythoes.
2.In a similar way, in the Bible, Dragon = Serpent = the Devil.
3.BUT in the Hermetic, gnostic, alchemical, esoterical tradition, the Devil is the good guy. And has two faces, the Red one (Chaos) and the Gold one (Law) . Dungeons & Dragons is a game inherently informed by this tradition, so one can say that both chromatic and metallic dragons, both Chaos and Law, are expressions of the same principle, as yin and yang
As Marandahir notes:
Yellow or Gold Dragon of the Center in Chinese mythology aligns heavily with Law.
Gygax mentions that the good dragons are inspired by east Asian myths.
TSR - Q&A with Gary Gygax
This is the multi-year Q&A sessions held by D&D co-creator Gary Gygax here at EN World, beginning in 2002 and running up until his sad pasing in 2008. Gary's username in the thread below is Col_Pladoh, and his first post in this long thread is Post #39.
www.enworld.org
The 1970 edition of "The Book of Imaginary Beings" by JL Borges and M Guerro has sections on Chinese Dragons, Eastern Dragons, and Western Dragons. The section on Chinese dragons says:
It doesn't name any though.
The section on Eastern Dragons mentions Celestial Dragons that carry the palaces of the gods on their backs, Divine Dragons that make "winds and rain for the benefit of mankind", Terrestrial Dragons that "determine the course of streams and rivers", and Subterranean Dragons "stands watch over treasures forbidden to men". There are five Sea-Dragon Kings, "the chief is in the middle, the other four correspond to the cardinal points". It also doesn't name any.
Barber's "Companion to World Mythology" lists some by name - but it is in 1979 and so outside my range. I'm looking for in the older age range that gives names.