I'm not sure it's possible to get the swing component from a Document. But the issue is easily solved: just add a different instance of the listener to every text field, and store the text field in the listener itself.
textField1.getDocument().addDocumentListener(new MyDocumentListener(textField1));
textField2.getDocument().addDocumentListener(new MyDocumentListener(textField2));
textField3.getDocument().addDocumentListener(new MyDocumentListener(textField3));