And a good imagination! If you have heard your family name spoken aloud in Yiddish you are lucky. Imagine how it would have been written in English, or Spanish, or Russian. Then imagine how it might have evolved through the impatience and typos of border guards, boat manifest recorders or census takers. And finally consider how it would have been Anglicized , Spanishized, Russianized, Prussianized etc. ( Romanized) by choice, to allow people to fit in better ( or to hide) in a new place.
The following is a list of names found on the net. Each has a definite connection to a town in the area of Poltava (Russia or Ukraine); modern border changes have been ignored.
Poltava may have been a centuries old home for your family (e.g. Khorol) , or a stopping off place while being chased out of Poland or Lithuania and onto the immigration ships to New York, or Quebec or anywhere at all.