I see a problem. Kasia is not a name it is a short form.
Yes I know this but it's similar to how Kate has become a name in it's own right although it derives from Catherine/Katherine. Kasia has become a name in it's own right.
:) I'm Kasia and many of my Polish friends my age are Kasia. Americans spell my name in many ways, most popular is Kasha, Kasa, Kasya... I don't like to be called an English version of my name, like Kate or Kathy... Yes, my name is popular in Poland but no, I don't want to change it. It's my name since I was born, so it would be weird to use a different one...
One of my favourite names :) So it's your birth name or the shortened version of your birth name but Kasia was always used? You shouldn't use an English version of your name when Kasia is you actual name :) I have seen it spelled as Kasha here.
I think Kasia can become a popular name for British parents.