Is there a specific term for the association of certain verb(s) with certain nouns (as direct objects)?
These phrases are sometimes called "collocations". I don't know of a word for one element in the collocation.
As pointed out by others, the name for the phenomenon you've isolated is verb noun collocation or verb + noun collocation.
If you google these phrases, you should be directed to various sites which give examples. I know of no master list, but you could probably start to compile one yourself.