It isn't clear to me if the names reported are all patrons of this gun store/range or just people who buy guns. If the GS employees are selling a LOT of guns to straw buyers then the place probably deserves to lose its FFL. I am also unfamiliar with gun purchase laws in WI, but in NC, the local sheriff issues the purchase permits (unless you have a concealed carry license). Presumably, the sheriff does some background checks. If I were the sheriff, I would check the national records as well as local.
Now if the business is reporting the names of shooters who use the range then IMO the data would probably overload the police. Also if the information were gotten without a search warrant, it could possibly be thrown out of court and all evidence gotten as a result of it.
When I buy a gun I sign an affidavit that I am buying the gun for myself only and not for any other person. I cannot figure out how it could ever be proven though, that a person was a straw buyer, especially in a state that allows ftf sales.
If I saw that information in the newspaper about a range/gun store I did business with I would probably just go elsewhere. My local range just takes first names or nicknames. I agree that there is too much collecting of information about all aspects of our lives, but especially regarding gun ownership. I know of many law abiding citizens who own "clean" guns with no ability to be traced to them. I believe this is done purposely to avoid the government sticking its nose into business where it does not belong.