The protagonist is actually the anonymous narrator who meets the signal man and becomes involved in the fascinating story that the signal-man tells him. We don't actually know much about the protagonist: we are never told his name, and we know nothing of his occupation or way of life, except that he obviously likes to walk. However, what we can see as the story progresses is the way in which he changes through the course of the narrative.
Note the way that he responds to being told about the first ghostly apparition that appears to the signal man, and how he works to discount it:
Resisting the slow touch of a frozen finger tracing out my spine, I showed him how that this figure must be a deception of his sense of sight; and how that figures, originating in disease of the delicate nerves that minister to the functions of the eye, were known to have often troubled patients, some of whom had become conscious of the nature of their affliction, and have even proved it by experiments upon themselves.
The narrator is keen to find a reasonable explanation for the supernatural events that the signalman relates. He stresses science and advances in our understanding to reassure both himself and the signalman. However, in spite of this stance that the narrator takes at the beginning of the story, it is clear that at the end, the horrifying events concerning the signalman's death have convinced the narrator, as he points out the various coincidences that stress the truth of the ghostly apparitions. He has moved from incredulity to reluctant and terrified belief.
The protagonist is the one who spends the night in Lorraine Castle. They remain unamed throughout the piece.