That sort of thing had gone on for centuries before Ellis Island. When a peasant couple registered a birth in the parish church, the only sort of public record until about 200 years ago, the priest had to guess at how to spell the name. The illiterate peasants certainly had no idea. Add in the fact that the priest was often not a native speaker of the local dialect, or perhaps even language, and you got a lot of variations in family names.
I don't remember the details, but I have read of an instance of brothers, born in Central Europe, in the 1800s, with different spellings of the last names, because a different priest, or possibly the same one, guessed differently about how to spell the name the peasant family gave, when registering births several years apart.
Ah, yes, I can see how that would happen. Then, figure in all the other ways names change, and it can be difficult tracing one’s ancestry. I haven’t been able to trace mine back further than 2-3 generations to Ellis Island.