Many families changed either the spelling or the entire name to Americanize it. My father and his brothers switched from Slonimsky to Sloan sometime around 1940 or so. However, one uncle entered the Army as Slonimsky anyway, while Dad used Sloan. The other brother spelled the name Sloane. I assume they forgot to tell him the spelling.
BTW, there is no need to make a legal name change. Anyone can use whatever they wish as long as it is not for fraudulent purposes. Neither Dad nor his brothers ever had a legal name change. For that reason, when he retired, my aunt had to testify for Social Security that she knew my father under both names. And it gets more complicated as his first name on his birth certificate is also not the name he used. He didn't know why but in the 1920 census, his first name was already changed. We surmised that he may have had the Spanish flu and that his mother changed his name to fool the angel of death, a not-uncommon thing.