Actually, it was explained in the sequel “2010” that HAL was NOT derived from IBM, but from the words Heuristic ALgorithmic. The way it was explained leads me to believe that Clarke was NOT happy with people making that connection. If I remember correctly, it was Dr. Heywood Floyd that talks about it in the story.
The Daisy song was sung by HAL as he regressed back to “childhood” because his storage modules were being removed by Dave Bowman in order to release Discovery from HAL’s control. HAL had become murderous because of a conflict between priorities in his programming(Keeping the true nature of the mission secret vs the stated mission and keeping the crew alive). This is also explained in 2010 when they introduce the Dr. Chandra character.
“Dr. Chandra, I have a question.”
“Yes, HAL. What is it?”
“Will I dream?”