I will share with you one of my own interesting family stories, which will illustrate to you how the path to discovering the history of one's family name can be convoluted and the process daunting.
My beloved maternal grandfather was born Avraham Chone Gniazdowicz. He was born in or about Sniadowo, Poland (there was an adjacent shtetl named Gniazdowo, which presumably is how his family came by their surname). He immigrated to the U. S. with a cousin in 1906, though not as a Gniazdowicz, but as an Oschensky. This was the family name of his cousin Shloime (Sam), with whom he immigrated with (note that his cousin at some time after arriving in the U.S. changed his surname too -- from Oschensky to Ocean).
Presumably grandfather (as a fifteen-year-old) changed his surname while still living in Poland in order to avoid the draft, though perhaps there were other reasons, e.g. the lack of a birth certificate. Perhaps he took the surname of his cousin's family and used the birth certificate of a male in the Oschensky family who had previously died, or because they had no need of it, for whatever reason. One can only guess....
I imagine the reasons for why someone changed their name (or had their name changed) often were not discussed openly within one's family, for whatever reason. Perhaps some were afraid that if the reason for the name change was discussed, it might tarnish their imagine. Maybe worse yet they feared, if discovered by the "wrong people", they might be deported back to the "old country". Or perhaps the name was changed so long ago, it was "in the past" so to speak. To talk about such things might bring more to their consciousness the family they sadly left behind, family events they might not want to talk about, etc.
Let's return to my grandfather's situation. He came over to the U.S. with a different family name, though when he arrived in the U.S. (met by his cousin's father, who had previously immigrated and met yet other relatives on their arrival at Ellis Island), he changed his name back to Gniazdowicz, then quickly to a shortened version of this hard-to-pronounce surname -- now he was a Ness (No relation to Elliot).
Not only this, but on the 1915 New York City census (while living on Monroe Street on the Lower East Side, at the foot of the Manhattan Bridge), he is listed as "Abe" Ness (from Avraham), though this is the only time I've seen this given name of "Abe" used for him, as he subsequently called himself "Harry" (from Chone) in all other documentation. He was known as "Harry" as far as I know till the end of his days. He, my grandmother and uncle moved to Brooklyn in 1918.
So I knew my maternal grandfather as "Harry Ness", who had, by the way, another immigrant cousin who he was close to, who also lived in Brooklyn, also named Harry Ness (I still don't know the common ancestor between them), though his Yiddish given name was Chone Yankel.
This is another example of how family names evolved. Hopefully you know about your ancestors at least as much as I know about my maternal grandfather.
It can be then, for the genealogist, a challenge to gain information on a subject due to all the possibilities relating to how one's family name might have been changed (and sometimes not just once). It goes far beyond the question of whether a person's name was changed at Ellis Island, or at some other place, at some other time.
As they say, "It ain't easy"....