Which could also be the middle name of the originator - especially if his Polish surname was beyond anglicization, so to speak.
I only know one famous example of this - Józef Konrad Korzeniowski became Joseph Conrad to English readers - but perhaps the phenomenon is more widespread (it certainly is with noms de plume for actors, writers and musicians).
@Polonius3, this is your department - thoughts?
It's a toss-up. One never knwos what went through the heads of name-changers, whether someone put them up to it or what.
I knew pf an Aleksiejczuk from Podlasie, one of whose sonds in America whose sons changed it to Alecks and anotehr to Aleks.
If we assume the name-changer hovered round the original root to create Alexander, then it could have orignally been Aleksandrowicz, Aleksandrowski, Aleksandrzak, Aleksandrów, Aleksy, Aleksiak, Oleksy, Oleksiak, Sendrowicz and maybe even Nowak, Kowalski, Piekarczyk or Stasiak. Whimsical changes unrelated to the orignal surname were not uncommon. Someone the immigrant admired may have been named Alexander Caldwell and he thought his Christian name woiuld make a good surname.
All this is guesswork unless you caaeither find some Old World documents for your ancestor or talk to the oldest surviving relative or family friend who might know something.
BTW more than 800 people in Poland use the Aleksander surname.ł