Please do take a look at his arrival manifest. I think it is PANKO but transcribed as PAUKO.
If he was naturalized than his intent & petition would confirm. He used PANKO spelling, right.
Which "Russia" you think you are going to with the research? As you know, the Russia of old can now be, depending on the location, Poland, Lithuania, Ukraine, Belarus or Russia.
It would seem that your cousins have transliterated the surname into Cyrillic so than that is what you are looking for.