TÜV is the largest such organisation in Germany and almost has a monopoly. The inspections themselves are colloquially even called "TÜV", even if you do it at some other org.

However, as others have written, there is still some huge bias in those numbers. Especially German brand car shops provide an inspection service, where they pre-check and repair the car before the official inspection. Many of those German brands are also very big on company leasing, to the point where almost nobody buys a new BMW, Mercedes or Audi privately, they either get a new one as a company car via company leasing, or they get a used leasing return car. All those leasing cars always have the aforementioned inspection service as part of the leasing package. So those numbers are to be taken with a huge huge grain of salt.