May I ask you if you changed you name in the foreign country too?
sorry for such a late answer.
whatever you are allowed to have two different passports (of different countries) with different names- well, it is somehow a grey area (or maybe I do not understand the law). remember- your, let say, US ID doesn't really matter in Poland if you also have a Polish one.
I've changed my name (from, let say, Jan Kowalski to John Smith) first in the UK (where I chose to settle)- I did it through the deed poll. I don't really know where are you from, but in the UK one needs not to bother the courts if one wishes to change their name- deed poll is enough (of course- signed by the witness!).
After I've got issued with the British passport- under my anglicized name and surname- and after I changed my driving license (de facto main ID card in the UK) I went to the Urzad Stanu Cywilnego (USC- not UPC which came I have no idea from tbf) of my (former) town where I used to live- and wrote a letter basically stating that since I am a resident of other country, and I do have dual citizenship, and since I actually use my new names I wish to change them in Poland as well. As a proof I have provided my passport and driving license which were photocopied there- btw, the admin workers there were really helpful and nice, I couldn't say a bad word about them even If I'd like to do so; well, anyway- the permission was granted by- AFAIK- the Wojewoda (I'm not sure about that: the only thing I'm sure is that it was still a request that could be refused; unlike in the UK where you just state that you are no longer JK but JS /and setop using your old name/)- anyway, since I was born in different part of Poland they have to send some papers to the USC where I was born to change my (Polish- as I have no other one) birth certificate; they have changed it and put my new name and surname on it. Than I got a full copy of it (pelny odpis aktu urodzenia) and filled documents to get my Dowod Osobisty (ID card- as it's more conveniant to carry it than passport) which was issued quite quickly (not that I was in the rush or anything).
I hope I helped you, somehow. If you have any more questions, do not hesitate to ask them.