My last name is Vazuka, but it is polish and was anglicized upon arrival to the US.
How do you spell it in Polish?
How do you pronounce Vazuka in Polish?
Genealogy & Family History Stack Exchange is a question and answer site for expert genealogists and people interested in genealogy or family history. It only takes a minute to sign up.Sign up to join this community
There is no simple way to determine the original name with any accuracy from the information you have supplied. This is partly because there would have been no single event, such as an arrival, during which the name was formally changed from one spelling to another, although the spelling on arrival may well have been anglicised. The idea that names were officially changed on arrival at Ellis Island, or anywhere else, is a persistent fiction - the passenger lists were assembled long before arrival, as has been mentioned in the comments, and nobody would have been checking if someone used the exact same spelling as on the passenger list once they'd moved to Wisconsin or wherever.
It is more likely that in early records such as census and civil birth and marriage records and yes, immigration records, you will find multiple spellings as various recordkeepers attempted to render the name as they heard it, and eventually a spelling was settled on - perhaps because this was the spelling on a US birth certificate or other official document used through someone's life, perhaps because it was an easy and obvious spelling change (like a Jensen becoming a Johnson).
So the sort of questions you need to find the answer to are these:
As nkjt said, there is no simple way to determine the original name from what you have given us. Based on what I know of Polish names and pronunciation, your surname might have originally been spelt Waszuka, Waczuka, or Wassuka. I've confirmed these surnames are real using Google, but they are only educated guesses and I wouldn't want them to put you on the wrong track.
If they were travelling from the (then) Russian Empire, then their name could be first changed into cyrillic, then germanized in Hamburg (common harbour for migrants to leave from) then anglicized at the entry to US. And it might not have been a Polish surname in the first place (also not that rare with Polish families in XIX century). Documents - perhaps scans? - would be helpful. As a native Polish speaker I'm afraid 'Vazuka' does not look similar to any surname I know.