Dernhelm was the name Éowyn took when she was pretending to be a man in the army of Rohan when they rode for Minas Tirith. The name Dernhelm is not used in The Return of the King (film) because Meriadoc Brandybuck recognizes her immediately.
Trivia
She likely made up this name on the spot for Merry said "I can't tell who you are, sir, because your visor is down."