Nope cannot rename or move a model tab....
Try this VBA macro, it will rename all layout tabs to LayoutX where X is the indexed order...
Sub RNLayout()
Dim ACLayout As AcadLayout
Dim ACLayouts As AcadLayouts
Set ACLayouts = ThisDrawing.Layouts
For Each ACLayout In ACLayouts
If ACLayout.Name <> "Model" Then
ACLayout.Name = "Layout" & ACLayout.TabOrder
End If
Next
End Sub
If this is combined with my BrowseForFolder macro, you will be able to open a specific folder, open each drawing, change each one, save and close each one, all without user intervention.
To do so will require a little bit more code, but it is possible....