I wouldn't say so. "Function" is a pretty common term used to refer to somebody doing some specific task. There's an obvious correlation between an employee tasked with a carrying out a specific role or action, and a chunk of source code that does something specific.
And the same holds true for "variable". It's a very common term for things that change their state of being, including stuff that isn't directly related to programming or mathematics. Stuff like the weather, somebody's mood, and so on.
"Monoid" just doesn't have any everyday meaning like those terms do, especially a meaning that so closely resembles the programming concept like in the case of "function" and "variable".