> If we have a Monad `m`, we compute two adjunctions!
I guess you're talking about the adjunctions involving the Kleisli and Eilenberg-Moore categories. Reuben mentioned one of these.
I find these names incredibly intimidating given how simple the ideas are. In particular, the "Eilenberg-Moore category", with the longer and more intimidating name, is arguably the simpler idea. A bunch of us like to call the Eilenberg-Moore category of a monad the **category of algebras** of the monad, and the Kleisli category the **category of free algebras** of the monad.