Eva when the immigrants were called forward in turn they showed their landing card which contained their details including name, manifest page and number on page that had been copied from the original manifest on departure. The entries were then looked up on the appropriate manifest page. They had to confirm some details on the manifest and proceeded. It has been estimated that each immigrant might spend just 30 seconds with the clerk. See https://stevemorse.org/ellis/EllisMythNames.htm
It has been noted elsewhere that if you look at books about immigration published at that time or newspapers at that time (now searchable online) you will find no references to name changes.
So, we have many people repeating this story about name changes but several examples have been checked that show that those immigrants continued to use their original manifest names in subsequent census returns, marriage certificates etc and only later did they start using a different surname. I am not aware of any cases where there is documented proof that a name change took place at Ellis Island.
Until somebody can show documented proof that this took place the evidence does not support it. Please supply proof if you have some.
There are similar family tales of immigrants arriving in UK ports (Glasgow included) being told they had arrived in the USA and being duped by the crew to leave the ship. Again there is no proof of these claims and some of the claims are simply not possible.