Following most any creative crucible, there's bound to be some room for interpretation as to who did what. For all of the mystery that Batman embodies, the stroke-by-stroke of his genesis has been fairly well delineated by both Bob Kane and Bill Finger, the only two who were there.
They didn't do it at the time, however. For all we know, neither of them took notes that fateful day in the cold beginning of 1939. More than two decades would pass before the story would begin to unfold publicly on paper. (The real story, anyway.)
And when it did emerge, so did friction. But by the 1980s, some of the alleged discrepancies seemed to evaporate. The truthful center of the story began to solidify. The creations of certain supporting characters and villains were and still are disputed, but the who-did-what on Batman himself very nearly lined up, from the iconic cowl to the chilling origin. Bill never claimed he chose the name Batman. To our knowledge, Bob never claimed he chose the name Bruce Wayne.
There was one thing Bob did choose, a choice that has also never been disputed, which seems to me to be the most important thing for which he should be remembered. To quote a 1989 letter written by Bill's second wife:
"If Bob Kane called Bill in to write Batman, he certainly made a good choice, didn’t he?"
Thirty-seven years ago today, on January 18, 1974, Bill passed away. It would be some years before he passed into legend. Yet his legacy remains in limbo.
Lest ye forget, there is a way out of limbo. Tip your head even farther back, focus on balance, and keep moving forward.