I would imagine that as a child, the name change was quite fortunate for young Vito. If inquiries were made from Sicily for the young Vito Andolini, there would be no records of him having entered the US. Afterwards, as was said here previously, he was already established as a Corleone. Also, let us not forget the immigrant mentality not to mess around with paperwork.

The one thing that I do find interesting is that in the book, Vito took the name Corleone as a sentimental gesture to his homeland. I always wondered why FFC changed it, unless it was to show the immigrant's Ellis Island experience.