cleaning up obsolate names using For Each... In ... Next

I would greatly appreciate any help as I am totally stuck.

When I delete a Range (i.e. column) with named cells the names are not deleted.
I am trying to write a code to delete leftovers. So far I have:

Sub CleanUp()
    For Each Name In ThisWorkbook.Names
        If Name = "*!REF!" Then
           'Name.Delete
           Debug.Print Name
        End If
    Next
End Sub

I use the Immediate window to check if I get any hits and "Names manager" to confirm that there should be.

I have no idea what is wrong, as following works:

   For Each Name In ThisWorkbook.Names
             Debug.Print Name
   Next

as well as:

   For Each Name In ThisWorkbook.Names
        If Name = "=Sheet1!#REF!" Then
               Name.Delete
        End If
   Next