can I refer you to my earlier contribution to this thread?
A question you should ask yourself, is why is the town of Gunzburg called that in the first place? The probable reason is that there is a castle on the hill protecting the town, hence "burg"
The name of the river may be a local dialect, certainly the umlout lengthens the "u", so instead of "gun" the "u" sounds more like "flute". G and K can be interchangeable. The "n" will be soft, as it is in Germany today when I go there and say my name with a soft "n" and soft "s" I am clearly understood and my name gets spelt correctly.
So Gunz is a little different from Gins, and I am suspicious of the "z", which is hard not soft.
As for this being the origin of the name Ginsburg and all people with that name, I find this incredulous. Its far more likely that the name sprung up in lots of places in Eastern Europe, where German or Yiddish was the lingua franca. "Kings castle" can refer to one owned by a local lord or prince, of which there were many. In modern English, the equivalent would be Kingston, and there are towns (and people) called Kingston all over the English speaking world.
A point to reflect upon, is that Jewish people did not have secular/civic surnames, and only when coming into contact with civic society did they have to provide one (eg, a census, the police, a magistrate etc) Otherwise, they would be known as ben **** or bat ****. Its quite natural to take the name of your town, or better still, one that sounds posh.
Thus adding "sky" to the end is a Polish addition. (I think "ski" is the Russian equivalent) standing for "from" or "inhabitant of"