Can be called civil/Civil law notaries or Latin notaries. Civil law here means ‘kontinentaleuropäischer Recht’, legal systems based on Roman law.
In some Länder (German states), being a notary is a separate profession (Nurnotar), in others someone may be an attorney and a notary (Anwaltsnotar).
Notaries may witness signatures: this is called öffentliche Beglaubigung. Or they may draw up and execute a whole deed: öffentliche Beurkundung. It’s very misleading to translate either of these as notarize, the U.S. term for a notary public witnessing a signature. It’s also unclear whether beglaubigen or beurkunden is meant. I would say ‘notarially certified / certified by a notary’ for the first and ‘notarially recorded’ (for want of anything better) for the second.
Then there is the Beurkundungsgesetz, which could be translated as the Notarial Recording Act. That gives a better idea of its contents than Documents Act.
Another translation point that often throws translators who don’t know the law is the rule in section 3 of the Beurkundungsgesetz: a notary is forbidden from acting in matters if, for example, he has acted for the person in an unofficial capacity before. This is referred to in shorthand as ‘Vorbefassung’. Here is an example of its use:
‘Der Notar hat zu Beginn der Beurkundung nach einer Vorbefassung im Sinne
des BeurkG gefragt; diese wurde verneint.’