The U.S. Department of Homeland Security (U.S. Citizenship and Immigration Services) hosts a website with a "History and Genealogy" section. Here's an article from their archives: "We know from experience that records of entry of many aliens into the United States contain assumed or incorrect names and other errors." From INS Operations Instruction 500.1 I, Legality of entry where record contains erroneous name or other errors, December 24, 1952. Among the reasons for the "incorrect" names were the immigrant's using:

• A fictitious name
• The name of another person
• The true name in a misspelled form
• The surname of the stepfather instead of the natural father
• The surname of a putative father in the case of an illegitimate child
• A nickname
• The name used because of foreign custom, such as the given name of the father (with or without prefix or suffix) for the surname, the name of the farm, or some other name formulated by foreign custom
• The maiden name instead of the married name
• The maiden name of the mother instead of the father's surname 

When an immigrant's new name no longer matched that shown on their official immigration record (ship passenger list), he or she might face difficulties voting, in legal proceedings, or naturalization. Some sample letters representing typical mis-match cases can be found on the website, (as can an essay about American names written for the Fourth of July): http://www.uscis.gov/history-and-genealogy/genealogy/genealogy-notebook/immigrant-name-changes#letters Our thanks to web-surfer Fern for this lead.