Do car rental companies provide the environmental badge required for driving in the green zones in Germany?
Yes. If you rent your auto from a reputable agency in Germany, the proper license will come with the car. If, however, you rent outside of Germany and drive into the country, your car will most likely not be compliant. For peace of mind, you could inquire at the rental desk when you land in Germany just to be sure, but you should be covered.
Wherever you rent your car, ask about the permit before you drive away.