Tennyson envisions moonlight falling on Arthur's grave and lighting up his name carved into the gravestone, along with the dates of his birth and death. That same moonlight is also falling on Tennyson's chamber. Maybe the speaker takes some comfort in this?
The coming day also shines over both of them, but no—there doesn't seem to be much comfort here.
Check out how Tennyson uses imagery relating to "gray" (which we're sure you'll agree is a dreary, lifeless color), "dark," and "ghost[s]." These aren't upbeat images, folks.