Dernhelm was the name taken by Eowyn of Rohan when she disguised herself as a man and followed her uncle, King Theoden, to Gondor with the rest of the Rohirrim. She took Merry with her, hidden under her cloak, and together they defeated the Witch King of Angmar. Here are a few passages about Dernhelm from RotK:
One looked up, glancing keenly at the hobbit. A young man... less in height and girth than most. [Merry] caught the glint of clear grey eyes; and then he shivered, for it came suddenly to him that it was the face of one without hope who goes in search of death.
Unnoticed a Rider came up and spoke softly in the hobbit's ear. "Where will wants not, a way opens, so we say," he whispered; "and so I have found myself... You wish to go whither the Lord of the Mark goes: I see it in your face."
"Do you not [know my name]?" said the Rider softly. "Then call me Dernhelm."
But Theoden was not utterly forsaken. The knights of his house lay slain about him... Yet one stood there still: Dernhelm the young, faithful beyond fear; and he wept, for he had loved his lord as a father.
It seemed that Dernhelm laughed, and the clear voice was like the ring of steel.
Eowyn it was, and Dernhelm also. For into Merry's mind flashed the memory of the face that he saw... the face of one that goes seeking death, having no hope.