I think the place the name was changed was at the port of embarkation, like Hamburg or Cherbourg.  The story devolved into Ellis Island because that was the universal place that most remembered.  It was used even by immigrants who landed earlier than Ellis island opened...like Castle Garden.  The story is too common for it not to have happened somewhere and those ship's manifests I've read online are handwritten (scrawled) then folded and unfolded, got wet until it was quite a feat for the immigration at intake to read at all.  Mistakes were made, people traveled under false papers.