I don't think there were "common" name changes. Every family was so different as to its preferences and reasonings, etc.
I HAVE heard that if the European name meant something (such as a color or animal or occupation, etc.) then sometimes they Americanized their name to the American word for it (Green, Wolf, Miller, etc. etc.)
You don't say when they came over -- Would they have been in any US Census afterwards? If so, have you tried searching for them by first names and approximate birth years (no surnames.)
I've found people by putting in their first name and their parents' first names, too.
Post what you know about them and other ancestry.com users may know something/suggest something...(I'll try to! :) )