There may be quite a few spelling variations, in the old country as well as in North America. Could it be that the name in the old country was spelled Forek, with a diacritic called a hacek on the letter r? The Czech language has this letter. Do the Slovaks have it too?
This letter is pronounced like rsh, with the r and sh spoken simultaneously. I have it in my first name which is Bedrich (Fred). The letter has to be spoken quickly. If it cannot be pronounced 100% simultaneously, the letter r comes first, never the other way round.
Hungarian or German might change the spelling of the name to Forzsek, Forcsek, Forczek, Forschek, and more possibilities.