Unless they were in a witness protection program, the US Govt did NOT change any names of immigrants. That is a persistent myth.
Where is the "below is a letter with the families US name".
You don't give much information..... names, birth dates, birth countries??
Did they become citizens? If so, send an email to the nearest National Archives branch where they settled and they might find those papers if you provide adequate information.
Family recollections are notorious for being inaccurate.
and by the way, a search on Szule on FamilySearch brings up alternate spellings like "Sewel" and "Sewal".