Murray won't. Michel Therrien did not have his name on the Cup when the Penguins won in 2009. As far as could it? I know there's an appeals process where players and staff can get their name on should the people on high agree with the reasoning but not sure if that applies to fired coaches.
I don't know if the scouting staff gets their name on the cup, but they absolutely get Stanley Cup rings. I have a feeling the Kings will petition for Gagne and the league will approve given his history with the NHL. Either way, everyone will get a ring other than Jack Johnson, obviously.
“Every good army needs a couple of criminals.” - Dean Lombardi