When people use the expression "he's on autopilot" they tend to mean someone who's just going through the motions without being mentally engaged. In a popular sense, autopilot is used for any task that is running without active engagement. E.g. a business running on autopilot, to mean a business functioning without active engagement. What matters is how the term is popularly used, not how it is used in a particular technical context.
I suspect the real reason Tesla wants to hang on to "Autopilot" term, is that it allows them to subtly market this function as a self-driving vehicle without explicitly saying so by playing on the misunderstanding of the term by laypeople. This allows them to have it regulated as a cruise control device, instead of the more stringent safety and reliability standards that a self-driving car would have to meet.