is there a word for this very common form of noun

nouns that are derived from verbs, usually by putting "er" after the infinitive, to represent the subject of the verb doing that verb

runner from to run, drinker from to drink, invigilator from invigilate

similarly for when the noun is the object, employee from to employ

i would be particularly pleased if you could tell me in german, because no way is bestrafer correct german ronette, whatever rammstein say

Yeah, they're called agentive nouns.

it's a participant noun, i believe, but i think that's a really outdated term or something because i cannot seem to find anything on it. i know i've heard them called that (perhaps in a grammar class i've had? i don't know).

EDIT: desdemona is correct; i suppose whomever taught me "participant noun" made it up?

the -er german nouns are perfectly correct:

bestrafen/Bestrafer
schreiben/Schreiber
lehren/Lehrer

etc.

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