I think only the FQN is ever returned, store the me in a string and use .LastIndexOf(".")+1 to get the module name:
B4X:
...
Log(ModuleName(me))
...
Public Sub ModuleName(Obj as Object) As String
Dim psActName As String = Obj
Return psActName.SubString(psActName.LastIndexOf(".") + 1)
End Sub
If in a future update the way the module reference is created changes, then the code will break.
Using a constant, the module name can even be something more meaningful and not necessarily the actual module name.