Paddy. who comes from a largish family, used to refer to his siblings by number ("my first sister" etc.). He now speaks of the cats in the the same way: "Cat One" and "Cat Two". I regard this as invidious. If we cannot be bothered to call the kitties by their names, Janeway and Kirk, then we must say "Cat One" and "Cat Other One" (I'm not sure which is which).
My boss would understand. We are planning a team visit to one of our facilities but have to split into two parties because of space restrictions. He has designated these "Team A" and "Team 1".