Not quite the same thing, but languages (like German) that build up words for complex concepts by forming big words out of little ones are called agglutinative[1].
German is not considered an agglutinative language (you can google it if you don't believe me). German has long compound nouns, which isn't really the same thing.
English has long compound nouns too, by the way. You can make basically arbitrarily long nouns like "chief regional dairy inspector" in English. In German you would write this without spaces between the words. That's just a typographical convention, not a linguistic difference. It doesn't mean German's structure is fundamentally different from English's, and isn't what linguists mean by "agglutination".
If I recall correctly from my very limited knowledge, German is not really agglutinative, as it mainly just has the ability to combine preexisting nouns together into one word, while agglutinative languages take a root and then add a pre- and suffixes to build up new words related to the meaning of the root.
Taking the 7th example from this table [1], while you could theoretically construct something like "erfolglosenmacherwerden" in German and have it still sound somewhat comprehensible, that is not something that is actively done in the usage of the language and would sound about as strange as coming up with "to unsuccessfulmakerbecome" in English.
[1] https://en.wikipedia.org/wiki/Agglutinative_language