Although it is often conjectured that the name HAL was based on a one letter shift from the name IBM, this has been denied by both Clarke and 2001 director Stanley Kubrick. In 2010: Odyssey Two, Clarke speaks through the character of Dr. Chandra, who characterized this idea as: "tter nonsense! [...] I thought that by now every intelligent person knew that H-A-L is derived from Heuristic ALgorithmic".[2][3]
Clarke more directly addressed this issue in his book The Lost Worlds of 2001:[4]
As is clearly stated in the novel (Chapter 16), HAL stands for Heuristically programmed ALgorithmic computer. However, about once a week some character spots the fact that HAL is one letter ahead of IBM, and promptly assumes that Stanley and I were taking a crack at the estimable institution ... As it happened, IBM had given us a good deal of help, so we were quite embarrassed by this, and would have changed the name had we spotted the coincidence.