https://www.smithsonianmag.com/smart-news/ellis-island-isnt-...
https://www.nypl.org/blog/2013/07/02/name-changes-ellis-isla...
I don't believe this was a common thing to do upon arrival -- it was more like, when they wanted to open a business and be perceived as more American, more established, more trustworthy. It might not even be the immigrants themselves but their second-generation children, or even third generation.
If you visit a cemetery with lots of 1800's gravestones, it's pretty wild to see crazy diversity of last names from all over Europe, that we just don't have any more. Ellis Island didn't simplify or change anything. And which shows that in many of those cases, it was indeed the children who changed their name.
I always find it funny they did such a bad job of anglicizing it. Shuford doesn't really sound any more English to my ears.