Notified bodies are government accredited, mostly private companies that take over sovereign tasks on behalf of national authorities.
„‘conformity assessment body’ means a body that performs third-party conformity assessment activities including calibration, testing, certification and inspection;
‘notified body’ means a conformity assessment body designated in accordance with this Regulation;“
E.g. typical tasks of notified bodies include:
That means that notified bodies such as the TÜVs act decisively on the "approval" (a conformity assessment by the manufacturer itself) of medical devices.
The balancing act, that the notified bodies have to deal with, is that on the one hand they are in competition with each other and might be tempted by winning customers (the Medical Device Manufacturers) through generous checks.
On the other hand, they are being checked themselves (in the past (too) laxly) by the authorities and must therefore ensure that no safety-critical products are placed on the market.
If you need an overview of the notified bodies (in Germany), please check out the website of the DIMDI, the German Institute for Medical Informatics, a government organization belonging to the German Ministry of Health.
Additionally, the EU website is recommended. This site will not only help in the search for countries, but also in the search for the directives, which the Notified Bodies are accredited for.
For more information, you can check out this site about notified bodies in EU and their "accreditation scope".
Please be aware that there are institutions with accreditation to certify quality management systems, even according to ISO 13485. However, some do not have an accreditation to certify according to MDD respectively MDR. This is the exclusive right of notified bodies.