Cirroc reader Dave notes that the name was spelled Manchowsky once the family came to North America, to distinguish Polish from Russian. This distinction is partly moot because, as Dave points out, "Jews were not really Polish or Russian, they were just Jews." And I'm not a linguist. But I suspect Mienckowski might be more correct given Lomza's proximity to the then-Russian, now Belarusian border.
Of course if you use the Cyrillic spelling, all of this becomes moot once again.
I may consult my old college Russian lit professor on this matter.