While ensuring that the dropdown for player ownership updated when the civ assigned to the player changed, I realized a lot of other dropdowns/lists don't update in the equivalent case. For example, renaming a civ does not cause the "Available To" on the Unit tab to update to the new name.
While not critical sense everything will be updated on reload, it is slightly inconvenient, particularly if you rename a lot. A list should be compiled and these should be updated.