What is the name of the ship of Eärendil?

The ship of Eärendil was Vingilot, also called Vingilótë. Eärendil built the white ship with the help of Círdan the Shipwright during the First Age.

Eärendil used Vingilot to sail west across the Great Sea in search of Valinor, the realm of the Valar. He hoped to persuade them to aid the Elves and Men of Middle-earth in their war against Morgoth. His wife, Elwing, eventually joined him and brought with her a Silmaril rescued from the destruction of the Havens of Sirion.

Guided by the Silmaril, Eärendil and Elwing reached Valinor. Eärendil became the first mortal to set foot there, and his appeal helped bring about the War of Wrath. The Valar later transformed Vingilot into a heavenly vessel.

Eärendil sailed it across the sky carrying the Silmaril, becoming the source of the light known in Middle-earth as Eärendil’s Star, or the Morning Star. The White Ship is a descriptive phrase, not the ship’s proper name, while Alqualondë is an Elven harbor and Eärrámë is unrelated.