I'm not sure how helpful intuitive names are in practice, especially when the real concept has nuances that it doesn't capture. What do you get by renaming Monoid "Addable" that you don't get from the first line of a tutorial saying "Monoids are things that can be added"? Then, once you've got the intuition, it's much easier to absorb the line further down which says "oh, but they also need to be associative and have a zero element" because you already have a separate name to file these new properties under. It also provides a precise name for further discussion.
Also, on the topic of names for Monads, the key difficulty there is that there are at least two distinct ways of thinking about them which can be applied in different cases. Some Monads are best described by their join (List, Maybe etc.) and some are best described by their bind (IO, State etc.).
Also, on the topic of names for Monads, the key difficulty there is that there are at least two distinct ways of thinking about them which can be applied in different cases. Some Monads are best described by their join (List, Maybe etc.) and some are best described by their bind (IO, State etc.).