If that common name sounds awkward, it's all my fault. I made it up thirty seconds ago. As far as fungi go, unless you are one of the deadly, gourmet, or extremely unusual varieties, you almost certainly don't have a common name.
What's special about these little mushrooms? Well, first of all, I do mean LITTLE: the caps on the smallest specimens here are about 5 mm across, the largest about 10 mm. Second of all, they aren't closely related to most of the other fungi that they do look like, and they don't look like most of the fungi that they are related to. Here is a sampling of other members of the Order Hymenochaetales, to which Contumyces belongs:
Furthermore, this species is "bryophilous" which means that the occurrence of this species is tightly linked to bryophytes (moss, in this case). Whether the interaction is parasitic, mutualistic (or something stranger and more complicated) remains to be seen.
This fungus wasn't thought to be particularly common in California until one of the core members of MushroomObserver (Darvin DeShazer) started posting photos of this species from his yard. Then, it seems, people started finding it all over (because we started looking for IT, and we started looking in APPROPRIATE PLACES). This goes to show how important and useful "citizen-science" initiatives like MushroomObserver can be (check it out).