We explicitly encourage the "let's invent name for this similar but unnamed thing" with our students, and use whatever name they come up with for the thing for

We explicitly encourage the "let's invent name for this similar but unnamed thing" with our students, and use whatever name they come up with for the thing for the rest of their time with us. Sometimes those student created names become legendary. They really enjoy the idea that they can have "Jane's relation" be used by students after they graduate. (Of course, sometimes Jane's relation is really Euler's totient function, and we have to encourage them that even though they found something a very good mathematician also found, we're going to call it by the common name.)