The Rome-Berlin Axis joined together Germany and Italy, and both signed the Anti-Komintern Pact with Japan, directed against the USSR ( unless Japan decided not to go to war with Soviet Russia after their defeat at Khalkin Gol in 1939 ) . Hitler declared war on the US after Pearl Harbor to get a free ride for his submarines against US Navy in the Atlantic. Some other countries like Hungary, Romania, Croatia, joined the Axis after Hitler's invasion of the USSR....Bulgaria in 1945 had declared war to the US, Great Britain, and Germany but never to Russia !)
After Pearl Harbor, the US , Great Britain ( the British empire, including Canada, Australia, NZ...) and the USSR decided to call their alliance " the United Nations"...The US asked China to join, and then many other countries ( Brazil,the occupied countries in Europe, etc ...). But France's Vichy government never joined a military alliance with Germany, alike Franco's Spain, unless both governments allowed voluntary troops to join the German army on the Russian front ( the legion Azul for Spain, and the LVF for the French )....