They can't own "gnome". They have a much better chance of owning "rock gnome that is highly intelligent, fairly resilient, have a life span of centuries, can see in darkness, is resistant to mental magic, knowledgeable about artifice, and is good at building clockwork devices"
Your point that the more distinctive a modification is, the more copyright protectable it becomes, is correct, of course.
I just want to look more closely at the public domain concept of a "gnome".
The term is an umbrella for multiple different cultural traditions.
"Rock gnome". The person who invented the word "gnomus", Paracelsus in the 1500s, used it as a name for an "earth" "elemental", a personality of the rock itself. So, a "rock gnome" is a tautology and public domain.
Afterward, many cultures used this Neo-Latin term "gnomus" whenever translating their own local traditions about "land spirits" and "sprites" into Latin as the language of scholars. So, "gnome" came mean many very different things, depending on context.
"Highly intelligent". Some traditions, such as leprechaun, portray the land being as a clever trickster. One also sees the connotation of intelligence in the popculture phrase of the "gnomes of Zurich", referring to international bankers and similar.
"Fairly resilient". Tough as a rock − as an earth elemental is.
"Life span of centuries". Many (most?) of these creatures of reallife folklore beings are immortal, such as capable of being injured but as a spirit incapable of dying, or other characterizations of immortality. The idea is, they exist as long as the rock or land exists. A long life span is public domain.
"Can see in darkness". In 1712, a definition of "gnome" is, "a dwarf-like earth-dwelling spirit". As a creature of the underground that lacks lanterns or torches, it is understood that gnomes can see in the dark, in some sense.
"Is resistant to mental magic". At the moment, I cant think of a reallife public domain tradition that refers to a gnome having mental resilience. But at the same time, for the same reason, mental resistance doesnt feel especially "gnomish" to me. If mental magic is what makes this gnome distinctive, it might make more sense to call it a "psionic gnome" rather than a "rock gnome". Then again, the Norwegian and Swedish gnome (nisse, tomte, etcetera) is psionic, being a "mindful" presence and influence.
"Knowledgeable about artifice". British gnomes, such as brownie, are industrious and make things, including shoe makers.
"Building clockwork devices". Gnomes can relate to mills that grind grain, and later machinery. Specifically a clock maker would be an example of such mechanical artifice.
Note, the popculture "garden gnome" appearance orginates as a Dutch tradition.
As you can see, the D&D gnome concept is a fairly straightforward import of public domain concepts about the "gnome".
In the case of the "gnome", it is easy to write up your own description of a gnome without any copyright issue. You might tweak it for good measure, such as highlighting its "earth elemental" traits or that it is a "faerie spirit" depending on which reallife tradition one leans into, or make it radically unique as your own recognizable modification. But pretty much any version of a D&D gnome that you reinvent is going to be safe.
These are the two other areas I asked for corrections / removal
