No, names were NOT changed at Ellis Island (for all you latecomers who arrived there, my family came in 1868 and 1872).
Ships passenger manifests were compiled at the port of Embarkation in Europe and went from the ship to the immigration authorities at Ellis Island. Immigrants were processed with the names they used to board the ship.
Many immigrants assumed Americanized names upon landing in Manhattan or elsewhere after leaving Island.
My late FIL, left Hamburg with his first name o. The manifest listed as Erich. As soon. As he settled in the US he Americanized the spelling to Eric (I not discuss family name whose ending changed from ch to ck). When becoming a citizen he was permitted to formally change his name without having to go to court and pay fees.