Actually, the "Americanized" names were mostly picked by the crew on board the steamship line (Cunard, White Star, Holland America, etc). The immigration inspectors just worked from the provided passenger lists.
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Also here is a third party search tool (that even ellis island website recommends over theirs): http://www.jewishgen.org/databases/EIDB/ellisgold.html
Oddly, even that third party form has an "old version you probably shouldn't use". (The link takes you to "gold". The old one is "white").
For extra laughs, take a look at the URL when you view the ships manifest images.
One is French Huguenot, though,and it's not so much anglicized as just misspelled. It certainly would have marked them as French, but I wonder how much of it is just chalked up to poor literacy on all sides.
It even mentions: " However, many last names were altered slightly due to the disparity between English and other languages in the pronunciation of certain letters of the alphabet"
Unfortunately their source [34] is a link that does not exist anymore at that URL