In fact, no names were written down at Ellis Island—the people coming to the US were required to provide their contact information when buying the tickets for the journey, so their names were already recorded in the ship’s manifest. Families might have changed their names after settling in the new country.
You can blame a scene in The Godfather II for popularizing the urban legend.
@Madken65 Ellis Island databases of ship manifests are available to search, and are worth going back to periodically.
An independent tool made by researchers is my go-to: https://stevemorse.org/ellis2/ellisgold.html