皆さま､ありがとうございます｡次のものを見つけました｡これによると､戦争の最初の段階で､自ら､United Nations と名乗ったようです｡
The text of the "Declaration by United Nations" was drafted by President Franklin Roosevelt, British Prime Minister Winston Churchill, and Roosevelt aide Harry Hopkins, while meeting at the White House on 29 December 1941. It incorporated Soviet suggestions, but left no role for France. Roosevelt first coined the term United Nations to describe the Allied countries. Roosevelt suggested "United Nations" as an alternative to the name "Associated Powers." Churchill accepted it, noting that the phase was used by Lord Byron in the poem Childe Harold's Pilgrimage (Stanza 35). The term was first officially used on 1–2 January 1942, when 26 governments signed the Declaration. One major change from the Atlantic Charter was the addition of a provision for religious freedom, which Stalin approved after Roosevelt insisted. By spring 1945 it was signed by 21 more states.
The Declaration by United Nations, on 1 January 1942, was the basis of the modern UN. The term United Nations became synonymous during the war with the Allies and was considered to be the formal name that they were fighting under.
ｱﾒﾘｶ､英国､ｿ連といった国は､United Nations という旗印を立てた､大義名分とした､というふうに読めます｡