To je jedna možnost

Simple answer: no. You'll find all sorts of solutions. I find simply "appointment:" works for both "vznik funkce" and "vznik členství". Which suggests that "zánik funkce" and "zánik členství" would be "removal:" (including self-removal, i.e. resignation). But you could just as easily go for "from:" and "until:" because in the context (where it appears in the výpis) it is obvious what is at play. Or even Czanglify it by translating it literally. And as for "společník", yes, in this situation (but not, say, at a law firm) your safest bet is "member".