The fictional star Tolkien described as the Silmaril-bearing star was Eärendil.
In Tolkien’s mythology, Eärendil the Mariner sails into the West carrying a Silmaril on his brow. The Valar set him in the sky, where he becomes the bright star associated with hope and guidance. In The Lord of the Rings, Frodo sees and invokes this light, especially in the Phial of Galadriel, which contains light captured from Eärendil’s star.
Eärendil’s story connects several ages of Tolkien’s legendarium. He is the son of Tuor and Idril, and his voyage helps bring the Valar into the final conflict against Morgoth in the First Age. Through his descendants, he is also connected to Elrond and Elros.
The name is sometimes confused with Gil-galad, Aragorn, or Beren, but those are different characters. Eärendil is a mariner, a bearer of a Silmaril, and the figure associated with the star of hope.