A pleasure to receive you message. The spelling is not definitve. On my father's citizen ship papers it was spelled FUDYM. On my mother's citizenship paper it was spelled FUDIM. Generally it was spelled acording to how the naturalization officer thought it should be spelled. My mother's name was Anna and I liked it so well I named my eldest daughter Anna too.
You must remeber that Poland as a country did not exist until it was created by the league of nations after WW 1. My parents would refer to the homeland as Russo-Poland. It was under the control of the Tzaar of Russia. That area consisted primarily of provinces which still exist.My parents provence was Lublim in the town of Bilgoraj. This was only one of about 2 dozen such contiguous settlements known as The Pale.The Pale of Settlement was the restricted area where by law Jews were allowed to live. Outside that area Jews were not permitted to live except by special exemption. By the year 1885 there were about 4 million jews living in the Pale of Settlement. More information is clearly presented in easy to read graphical maps written by Martin Gilbert and titled Jewish History Atlas.
Each town from that Pale of Settlement establisehd a burial society after a significant number emigrated to America. These cemeterys are predominately located in Brooklyn and Queens in New York City. Their records have a vast history of family relationships usually written in Yiddish which I can't read.