The most popular name for DemocraticUnderground--that is, the most popular name off my fellow alum's island--is "DUmmieland," whose origins are obvious.
The word has been around a long time, probably since circa mid-2001, but was popularized across the internet by P-J Comix's most-excellent DUmmie FUnnies on freerepublic.
"Skins's island," which is synonymous with "DUmmieland," was coined in late 2007, and is derived from "Skinner," the CEO of DemocraticUnderground, "Skins" having ostensibly been his nickname while playing rugby at Yale; and of course, "Skins's island" dovetails in nicely with the image of the DUmmies being primitives on a lonely island somewhere out in the vast seas.
Both terms are equally appropriate for use in all circumstances, but generally, "DUmmieland" is used when one gets the impression of Skins's island as some sort of fantasyland, wonderland, wolkenkuckucksheim, dreamland.
And, generally, "Skins's island" is used when one gets the impression of DUmmieland as being inhabited by cruel barbaric violent bloodthirsty savages and beasts who understand nothing but the lash.