Have you heard about Babbington? Badminton to you and me.
Ay,ay, ay, you are showing your Irish "brilliance" here, Atch. Badminton as a word and as a game came to Poland as late as in the 1960s. The word was (and perhaps still is) difficult for Poles, so they started to pronounce it their own way. Do the Germans reproach us that we say "gmina" rather than "gemeinde" (Dougpol1 would probably say they should as he admires everything what is German in Poland)? In my childhood I heard the pronounciation "babington" and to this very day I prefer it to the strangely sounding "badminton" despite knowing that only the latter is correct. Anyway, find me the former as an entry to a Polish dictionary and I will buy you a ticket to Dublin (a return ticket, bien sûr).
cottage cheese according to someone I know (who has third level education) is 'cut a cheese' and is so named for the action of cutting the cheese with a knife.
Now, here you are showing even more of your Anglo-Irish "brilliance", Atch. The world isn't a place rotating around the English language.True, English is the language of international communication, but that doesn't mean all nations should follow the Irish who abandoned their ancestors' tongue to the benefit of English. The concept of incountability is a very strange concept to the Polish, so they would always make mistakes regarding it. 'Cut a cheese' is a typical mistake for a Slavic learner, be it as funny as it must be to the British or the Anglo-Irish ear, but there is nothing to be surprised about on the linguistic level.
As to your original question, I couldn't find any answer for Mikołaj/Nikolai (or niedźwiedź/med'wed'). I think it goes beyond the palatization phenomenon.