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.