Oh i would say "ring" is in fact quite a descriptive term.

Apparently, in older german, "ringen" meant "to make progress of some sort/to fight for something". And a ring has two functions: addition and multiplication. These are the foundational functions that you can use to construct polynomials, which are very important functions. You could look at functions as a machine where you put something in and get something out.

In other words, you put something into a function, the function internally "makes some progress", and spits out a result. That is exactly what you can do with a "ring".

So it kinda makes sense, I guess.