"The original definition, in terms of a finitely additive invariant measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun." https://en.wikipedia.org/wiki/Amenable_group
I'm not a native speaker and I don't get the pun :)
It suggests a group of people who get along well with one another. :) I hadn't thought of @André's interpretation; pronunciation notwithstanding, I yield. :)