I have an example of how a first name got changed during the journey from Lithuania to the US, which likely could also happen to a surname.
I was looking into the couple Abram and Rose Schiffman, who came here about 1891 and whose children were all born here in the US, and who came from Lithuania, but where I didn't know. So, I was looking for a young couple, likely in their 20s, no children. And I quickly found an Abram and Therese Schiffman from Schalen (Siauliai) coming from Hamburg to NY, early 1892. What puzzled me was the name Therese, which I haven't seen before for a Jewish woman from Eastern Europe. Maybe this was the couple I was looking for, maybe not.
Luckily, I have a photo of the couple's gravestone here in the US, which shows Rose's Yiddish name as Etta Reiza. I believe what happened is when either the tickets were purchased or when the couple arrived at the ship in Hamburg, that when her name was pronounced, the clerk only heard 'Ta Reiza', and he missed the 'Et' part. So, her name sounded like 'Therese', and was written down that way. She and her husband must have been confused during their journey and at Ellis Island why her first name was suddenly Therese, which to them would have sounded like 'Ta Reiza'. or possible 'Ta Reiz'. Perhaps this had an effect on her going by 'Rose', here in the US.
But still, I also believe that immigration officials here in the US did not change names. Mistakes/Mis-hearings/Miss-spellings would have happened at other times, either when the tickets were purchases her in the US or Europe, or when they arrived at the German ports and gave their names to the ship clerks.
I have a great aunt Mollie (Yiddish name Malke), who traveled here to Philadelphia under the name 'Mary Lack'. I was puzzled by this until I found her older brother here in the US had purchased her ticket, and must have given the clerk the name 'Mary'. She must have been very confused as to why she kept being called by Mary during her trip.
Olitsky - Alytus, Lith.
Leybman/Leapman/Lippman - Dotnuva, Lith.
Lock/Lak/Lack - Zagare/Gruzd, Lith.
Kolon/Kalen/Colon - Joniskis/Zagare, Lith.