The name Undómiel was reference to Arwen's grandfather Eärendil; it was the light of the Silmaril on his brow that shone as the Evening Star (and also filled the Phial of Galadriel). The name also seems to carry a more symbolic meaning: as the Third Age came to a close, so did the time of the Elves in Middle-earth, and Arwen's shining beauty marked their passing as the light of the Evening Star marks the passing of day into night.