I did a little bit of... um, research... after making this thread, but too late to edit the OP so I'm posting this reply instead.
I
discovered that those aren't actually names, and are more like ranks. Ulaire Attea, for example, is Quenya for "Second Ringwraith." The others are "Third Ringwraith" through "Ninth Ringwraith," though I don't remember off hand which is which.
It almost makes me wonder what "First Ringwraith" would be in Quenya. I can understand why they called him the Witch King instead of some arcane Quenya name-that's-actually-a-rank, but I would be interested to know anyway.