I have been told that Wenner has something to do with Vänersborg (once Wennersborg), which is a town near Lake Vänern, the largest lake in Sweden, but others say it is connected with that lake. I am not sure, but it seems to me that the lake is a better reason for that name.
I have a Wennersten from Sweden who was married to my mormor (mother's mother) before she married my grandfather, so I have been trying to learn about the Wenner part of the name too.(The "sten" part means "stone".)I thought that Wennersten was uncommon but I think that Wennergren is even more rare.
The W in Swedish names is sometimes replaced by a V. The Swedish dictionaries have very few "w" letters.Wennersten is sometimes spelled as Vennersten or even Vännersten/Wännersten. (The letter ä sounds like e.)