Monad is definitely abnormally difficult to humanize. The trio (T, ∀ a. a -> T a, ∀ a b. (a -> T b) -> (T a -> T b)) is really hard to nail down.
I don't object to "mergeable" for Monoid, but I think I weakly prefer "appendable" since it seems to say a little more about how things merge (and of course the free monoid is exactly that).
Speaking again to the broader context, one thing I really like about Haskell's choice of naming these abstractions after the math is that this type of discussion has no bearing on what types adhere to the abstractions - we're not left arguing over whether Sum and Product are "really" appending, or set intersection is "really" merging. Integers are a clearly monoid under Sum and Product, and set intersection is clearly a semigroup but not a monoid (if our universe is open) because there is no identity.