I had this shower thought earlier and I actually wanted to post it in that community. The name I came up with was SmartWalkman, but later I realized that Walkman is Sony specific, so I doubt other companies would’ve gone for that name, but I didn’t want to let this shower thought slip so here I am now asking you guys.
For a brief period of time, they (mostly journalists) tried calling them App Phones to differentiate from other phones with touch screens. There was also the rumor leading up to the iPhone that it would be called the iWalk.