I see Fishman mentioned in the index of Sefer Dombrovitza (the Dombrovitz yizkor book), once on page 777 and once on page 696. Unfortunately, my Yiddish is very weak, so I can't tell you what's on those pages. If you know Yiddish, or know someone who does, it would be interesting to translate the pages and see if it's your family. You can find the book on-line here:
http://yizkor.nypl.org/index.php?id=1695You mention that when your father came through Ellis Island, the authorities probably didn't understand him. I suspect that is unlikely. At that time, they had many translators, and it was likely that he was admitted by someone who spoke Yiddish (or possibly Russian or Polish), and he likely had multiple forms of documentation to prove his identity. It's a common misconception that people had their names changed at Ellis Island. Rather, they just had them anglicized.
When I was growing up, depending on who I was talking to, Dombrovitz would be attributed to the Ukraine, Prussia, Russia, or Poland. It was definitely in Russia when my grandparents and aunt left there in the 1910s.