Did you know that going back to the Jagiellonian period certain Polish names were frequently given to neophytes, Jews who converted to Catholicism. Often these contained the roots of days of the week or months of the year in which the conversion took place. Such names included Majewski, Lipiński, Niedzielski, Poniedzielski, Piątkowski, Wrzesiński, Kwiatkowski, Kwieciński, Styczyński , Czerwińskimi, Sierpińsk, Grudziński, etc. Others included Nowopolski, Nowakowski , Nowicki and Dobrowolski, the latter suggesitng the conversion had been voluntary (by free will). Sometimes it was shortened to Wolski. None of this means that every bearer of the above surnames is of Jewish ancetsry, only that those names were commonly used by converts. Unconveretd Jews often used toponymic surnames such as Krakowski, Lubartowski, Lubelski, Gdański, Poznański, etc. which in Yiddish were Krakower, Lubartower, Lubliner, Danziger, Posener, etc.
I'm Polish Jew. I have got typical Polish name with "-ski". Durring patritions of Poland Jews hadn't their surnames, Germans obligatory were giving names for Polish Jews. To be Goldstein you had to pay bribe for German officer, without bribe you could end with name like Schnur or Apfel, many Jews had names form towns they were living that is why they simple changed it into Polish version.
After WWII our family chnaged name into Polish one.
I have always thought myself to be mostly Polish (according to family) however, after having my dna tested, Its seems on my mother's side (mtdna), there is an offer lot of similarities to the Ashkenazi Jewish genebase. Not sure if this is coincidence or if there is some real evidence for there. For what it matters, all I know is that my great grandmother's last name was £os, and she was from Białystok.