Say in the next couple of decades or so there is a major power war with global death tolls of at least 20 million or so but that all or at least most of todays nations emerge intact. Just as the United Nations replaced the League of Nations after World War Two what would be the name of a successor to the United Nations?
The Unified Earth Space Council (UESC). "The Unified Earth Space Council (or UESC) is Earth's body of government, also exerting control over Mars." https://marathongame.fandom.com/wiki/Unified_Earth_Space_Council
I have ideas for my successor to the United Nations. A General Assembly of 48 nations from which 12 nations become members of a Security Council for two years on a rotating basis. No single member of the Security Council has veto authority but in order for the Security Council to authorize military action 11 of the 12 Security Council members must vote in favor of it. I would also like to see a future successor to the UN having their own standing military force. Not an Army or an Air Force but a naval force modeled after the NATO Standing Naval Force Atlantic.
UN forces are as worthless as teats on a boar hog. When we'd go through UN-manned checkpoints in Iraq, we'd usually have to wake up the UN guards. The UN is a joke. If a country wants to do something, it will do it.
As long as any "UN MILITARY FORCE" comes from member states, it will. States all have their own priorities and won't send their own people into danger without those priorities being in consonance with UN objectives.
Have you forgotten the Korean War? Thousands of military personnel from nations not connected to East Asia in any way were sent into danger (thousands died).
The predominant view in the world in those days was the "Domino Theory" that held that if communism conquered one nation, others would fall "like Dominoes". The countries fighting alongside us in Korea were not there because the UN told them to be there. They WANTED to be there and simply got UN approval. Japan saw the spread of Communism in the region as a THREAT. Many countries did. Look at the Coalition we put together in Iraq. Every one of those countries VOLUNTEERED to be there. We started the ball rolling in Korea with the deployment of Task Force Smith from Japan when North Korea invaded South Korea. The UN had nothing to do with that.
What Would You Call a successor to the United Nations? An opportunity not to make the same mistake a third time.
I envisioned four international naval fleets. Each composed of 8 surface ships armed largely with SAMs and cruise missiles. As an added feature to such a force I envisioned each of those fleets with ONE ship carrying four cruise missiles armed with a small nuclear warhead (5 kilotons or so) Big enough to cause serious damage to a city but NOT big enough to threaten any kind of hardened military target.
Most battles are fought on land. Wars are ALWAYS won or lost on land. Unoccupied enemy territory is STILL "enemy territory". No war was ever won from the air without use of nukes. It takes a friendly Soldier brandishing a bloody bayonet standing astride the enemy Capitol for a war to end. Navies can only drive so far inland, by the way.