Visualization of US surnames by geographic location from National Geographic.  Originally seen at downlo.
English surnames (shown in blue) are the most common, but that it isn’t because the bulk of Americans are of English extraction.  German immigrants, one of the biggest groups of immigrants, often anglicized their surnames so Schmidt became Smith and Muller became Miller.  Miller is actually a far more common surname in the US (#6) than it is in the UK (#53).  Millers had a shady reputation in the UK but not in Germany, thus the professional surname is more common in Germany than the UK.  Scandinavian immigrants also made similar adjustments turning Johansen (#1 in Norway) or Johansson (#1 in Sweden) into Johnson (#2 in the US and #11 in the UK).
In the US, there is a myth of the “Ellis Island Name,” a misspelling or forced name change by immigration officials at New York’s Ellis Island.  However, Ellis Island was staffed so that immigrants were able to work with people who spoke their language and accurate record keeping was a priority.  That was not necessarily true of other ports immigrants entered, but largely name changes were done after arrival.
The most common last names for African Americans are also English surnames.  Some former slaves used their former master’s surname, while others are believed to have adopted the last name of someone they admired such as George Washington or Andrew Jackson.  A Huffington Post article about the history of Washington as an African American surname can be read here.

Visualization of US surnames by geographic location from National Geographic.  Originally seen at downlo.

English surnames (shown in blue) are the most common, but that it isn’t because the bulk of Americans are of English extraction.  German immigrants, one of the biggest groups of immigrants, often anglicized their surnames so Schmidt became Smith and Muller became Miller.  Miller is actually a far more common surname in the US (#6) than it is in the UK (#53).  Millers had a shady reputation in the UK but not in Germany, thus the professional surname is more common in Germany than the UK.  Scandinavian immigrants also made similar adjustments turning Johansen (#1 in Norway) or Johansson (#1 in Sweden) into Johnson (#2 in the US and #11 in the UK).

In the US, there is a myth of the “Ellis Island Name,” a misspelling or forced name change by immigration officials at New York’s Ellis Island.  However, Ellis Island was staffed so that immigrants were able to work with people who spoke their language and accurate record keeping was a priority.  That was not necessarily true of other ports immigrants entered, but largely name changes were done after arrival.

The most common last names for African Americans are also English surnames.  Some former slaves used their former master’s surname, while others are believed to have adopted the last name of someone they admired such as George Washington or Andrew Jackson.  A Huffington Post article about the history of Washington as an African American surname can be read here.