Here's some interesting background on the name "Alcoholics Anonymous," posted over at AA History Lovers Yahoo group, a forum I heartily recommend for anyone interested in the rich history and program development of AA.
May 20, 1938 -- the writing of the Big Book began.
June 15 1938 --Lois' recollection of the first time the term Alcoholics Anonymous was used (in "Lois Remembers" p. 197).
June 1938 -- Bill W wrote Dr. Bob: "By the way, you might all be thinking up a good title. Nearly everyone agrees that we should sign the volume Alcoholics Anonymous. Titles such as Haven, One Hundred Men, Comes the Dawn, etc. have been suggested." (This meant that the name "Alcoholics Anonymous" at that point was intended to be, not the title, NOT the official name of their group, but how the authorship would be given on the title page.)
Jul 15, 1938 -- "Pass It On" (p. 202) quotes from a July 15, 1938 letter from Bill W to "Messrs Richardson, Chipman and Scott of the Rockefeller Foundation" inviting them to attend a meeting at Bill's home on Clinton Street and said that in their case they would "gladly waive the [requirement of] heavy drinking that has qualified us for Alcoholics Anonymous," and consider them as "honorary members."
Jul 18, 1938 -- "Pass It On" (p. 202) Dr. Esther L. Richards (of Johns Hopkins) stated in a letter on that date that Bill W was using the name Alcoholics Anonymous at that time both as the working title of the book and as the name of the Fellowship.
Also in Harry Brick's story in the Big Book, "A Different Slant," Harry says, "The doctor at this hospital told me vaguely of the work of men who called themselves Alcoholics Anonymous and asked if I wanted one of them to call upon me." Since Harry probably got sober in June 1938, this also seems to indicate that the members of the AA group he contacted were calling themselves an "Alcoholics Anonymous" group, even if only at a casual and unofficial level.
Two early sources give a slightly later date for the title of the book -- October or November 1938:
Pass It On p. 202 -- most of the early AA people thought that it was Joe Worden, a writer for the New Yorker magazine, who first came up with the idea of using "Alcoholics Anonymous" for the actual title of the book, and Bill Wilson later on believed that the name "Alcoholics Anonymous" first became coming up in their discussions in October 1938. Joe was never able to remain continuously sober for very long, and ended up as a wet brain.
AAHL Message #1705 -- And Jim Burwell wrote in a memoir later on that Hank Parkhurst and Bill Wilson finally decided on the name "Alcoholics Anonymous" in the latter part of November 1938.
But in somewhat puzzling fashion, in the Foreword to the Second Edition of the Big Book (p. xvii), after describing how the first edition was published in April 1939, it then goes on to say: "the fledgling society, which had been nameless, now began to be called Alcoholics Anonymous, from the title of its own book."
May 10, 1939 -- about a month after the Big Book was published, the Cleveland AA group announced that it was splitting from the Oxford Group, and on May 11 held a meeting called a meeting of "Alcoholics Anonymous."
Late October 1939 -- Dr. Bob and the rest of the Akron group quit meeting with the Oxford Group, and began meeting separately, first at Dr. Bob's house and then, beginning in January, at King School in Akron.