Hi David,
You are correct in that any of the Mapbasic statements that add content to the Layout Designer include a Name clause. This includes Map From, Browse From, all of the Create statements like Create Text, etc., Add Image. Each frame of a Create Designer Legend also supports a Name clause.
Once a frame is created, you can use the Alter Designer Frame Id id Name "new name".
In beta 2 for version 17.0 the Frame Properties dialog now also includes a control to let you edit the frame name in the GUI.