In "Where Silence Has Lease", the Enterprise is trapped in a "void" by an entity which addresses itself as Nagilum. Is "Nagilum" the creature's name, or is it the species' name? Or perhaps both (as is apparently true with the Q)?
The official Star Trek Encyclopedia has this to offer on the subject:
Hole in Space - A spatial phenomenon created by the extra-dimensional being called Nagilum
The clear implication is that Nagilum is its name.
It is the name of the creature that spoke to Picard. The name is "Muligan" spelled backward, as actor Richard Mulligan was originally supposed to voice the creature.