Hi Johan
I'm going to move this message thread to the VSTO 2008 (Orcas) forum, as that's where the expertise is for that version.
As far as I know, the object model interface for the Shapes and InlineShapes haven't really changed in Word 2007. The new graphics engine wasn't fully implemented in Word, so it basically still uses what worked in earlier versions. You do have to distinguish between the two collections. They share some properties and methods, but not all. There has never been a Name or Visible property for InlineShapes; and it's not possible to bookmark a Shape. Perhaps that's where you're getting confused?
To allow the user to name a shape you have to provide the UI (all versions of Word).