Why do we call Chinese monoid "Chinese"? Why not "American"?
You can find the definition of Chinese monoid from Wikipedia. https://en.wikipedia.org/wiki/Chinese_monoid
I do not have the paper "Plactic-growth-like monoids" at hand at the moment but the history is correctly rendered in [J. Cassaigne, M. Espie, F. Hivert, D. Krob, J.C. Novelli, The chinese monoid, International Journal of Algebra and Computation, 11, (3), 301-334, 2001]
It was a question of M.-P. Schützenberger (MPS) to Krob and myself to prove (maybe at the cost of some additional conditions to be found), that only the Plactic Monoid had the same (multivariate) Poincaré-Hilbert series (PH-series) as itself. The first task was then to study the monoids (with multihomogeneous relators) having the same PH-series as the plactic. We found three series of ternary monoids. Now, if you arrange their relators along the hexagon formed by the permutations of "abc", one and only one of these series has the form of a triangle evoking the Chinese hat (here a triangle with angles of 30, 30 and 120 degrees). MPS used to call it "The Chinese hat monoid" which was eventually abbreviated as "The Chinese monoid".