Many families have a similar story of misheard names and misspellings at Ellis Island. Then, that new surname carried on for generations. Based on information from older relatives and old records, the first and last names of many of my Italian ancestors were changed there. Officials sometimes changed the spellings, dropped vowels, or wrote down the English version of a name. They had to process so many immigrants that they probably rushed them all through. To English-speaking ears, the Italian pronunciation of certain letters sound similar to each other. We think the officials misheard the names, and then our g-grandparents and grandparents just went with it. But, some old documents show different spellings.
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.
My grandparents were from a small village with only about 20 different surnames in use so even when the parish priest was from elsewhere he probably knew how to spell the names. But when my great-grandfather's brother died in a different village, his name was misspelled in the register of deaths.