Oh yeah, Poland's borders are rather flexible things as you go through history. I believe they're in more possession of Germanic territory than they were pre-reformation Poland, but a lot less Russian territory than at their height as the Commonwealth.

Ultimately, what I have to question is, the city was formed as Gdansk some time pre-1000 and was known as Gdansk for quite a long time. It then had a 300~400 year spell as some varieties of Germanic names similar to, but not quite Danzig, before becoming Gdansk again. And, in fact, in modern times it is known almost globally as Gdansk, with only Germany still referring to it as Danzig. So unless you're speaking German, which you're not, you have no real reason to call it Danzig.