All-American Comics, sometimes simply known as AA, was named after the All-American Comics comic book which starred the Golden Age Green Lantern, Alan Ladd Scott. Later this company evolved into DC Comics, which took its name from the Detective Comics comic book, which starred Batman (his first appearance was Detective Comics #27, by Bob Kane).
As an interesting side note, the feature character in both All-American Comics (Green Lantern) and Detective Comics (Batman), were both based in Gotham City, which was also the meeting place of the JSA.