My family tree goes back to a Harmon Neyman and quits altogether. My father Robert (b 1915) was son to Clinton (b. 1890), son to John William (b. 1864) son to Josiah (b. 1828) who was son to a William Neyman (no dates) who was son to a Harmon Neyman (likewise no dates). Do you know if your Harmon Neyman had a son named William? I am assuming that William was born in the late 1700's based on guessed generational spans.
Also, do you know how Neyman was pronounced? In my family it has been pronounced with a long I sound in the first syllable, but some Neymans have a different pronunciation (a long A sound, for example).
We have always thought Neyman was a Germanic surname, but have recently discovered that there are Neymans in Russia, and indeed a small town by that name. Do you have any information on this?