Doing a relatively quick dive, "berbalang" is one you might not expect to be public domain but is (it's Filipino), but it looks like the majority of aberrations are unique to D&D (helped along by the fact that almost all Quori are both non-mythically named and aberrations.) Almost all beasts just use common animal names which obviously can't be copyrighted, but there are a few that stand out like "fastieth" and "quipper" which are not common animal names. (Interestingly, "jaculi" is not--it's the plural form of "jaculus" or "iaculus," literally meaning "one who is thrown," referring to a dragon-like serpent creature or "javelin serpent.")
Interestingly, "couatl" is probably copyrightable, but "coatl" (no "u") is not, because it's just a Nahuatl word that means "serpent" (or "twin," apparently?) Likewise, feathered serpents in general can't be copyrighted, though making them specifically celestials might be tricky. Any angel with a word-mashup name is probably out, but angels in general and several of the types (archon, deva, planetar, solar, etc.) I'd say it's about 50/50 on whether any given celestial name (obviously not their appearance/nature/etc.) is public domain or not.
Constructs lean pretty heavily toward copyright rather than public domain, in large part because of the modrons, but there are plenty (e.g. golems) that aren't. As others have said, color + dragon and even metal + dragon is almost certainly not enough purely in terms of naming, since (for example) Green, Blue, White, Bronze, and Gold dragons (plus Brown) are all found in Anne McCaffrey's work and almost certainly some of them predate her. You might want to be careful about making "gold dragon" etc. actual categories per se, but the name alone is probably public domain.
I won't dig too much deeper, this has already taken a while, but yeah--some categories have TONS of non-copyrightable names, while others have very few. On balance, I'd say more are in the public domain than out, but it's hard to say and might depend in part on how exactly you define your criteria.