It seems that the governments of each nation choose their UN representatives however they want to. Is that correct? Was this also the case for the League of Nations?
Each government who was a member of the League would send an official representative who would be the equivalent of an "ambassador" from his home country. THis is just like the United Nations. Thus, if a government would change, they would officially appoint a new representative.
Since each government would handle its own internal affairs, the method of choosing the representative was left to the individual government.
The League would be made up of a General Assembly (representing all member states), an Executive Council (with membership limited to major powers), and a permanent secretariat.