I was going to add this to the "His name was changed at Ellis Island" thread, since one of the changes did occur at Ellis Island, but it was actually a correction.
As a gentile who has spent several years tracing my wife's Jewish ancestry (Thank You JewishGen and it's many great members), I've come to the conclusion that her ancestors were not as concerned about their surnames as they were about their patronymic names.
My wife's great grandfather Samuel was born in Siauliu, Lithuania as Schmerl NUDEL. He immigrated to Liverpool England where he married as Samuel NOODLE and had a daughter (her grandmother) born Fanny NODLE, they immigrated to Dublin Ireland (1896 - 1908) and used NOODLE on the census. He immigrated to the US in 1908 as Schmerl NUDEL and after arriving became Samuel NADLE. Fanny departed Londonderry for the US in 1909 as Fanny NADLE (UK Outward Passenger Lists). Her Arrival Passenger List shows her AS Fanny NODLE in route to her father Samuel NODLE. Her name is lined out on the passenger list and over written with Fanny NOODLE, his name is changed from NODLE to NOODLE and his address is updated so I assume this was done on arrival at Ellis Island when they verified her destination. (She is on the detained passenger list.) On the 1910 census she is Fannie NADLE. She married Hersh MARCUS (formerly MARKUS) in 1915 as Fanny NADLE. On the 1915 NY census she is Anna MARCUS. and from 1920 on she used Fannie MARCUS.
My Wife's great grandmother on the MARCUS side, born Pesa HIRSHFELD, married Israil MARKUS in Riga Latvia. She departed Liverpool for the US as Pessie MARKUS (UK Outward Passenger Lists) and arrived at Ellis Island as Pessie MARCUS on the arrival passenger list. She kept the MARCUS surname but alternately used Pessie, Bessie and Pauline for her given name.
Being of Irish descent, where you're surname represents your clan, it took me a while to absorb all the surname variations.