Oops! See the corrections below...

Example...
<aircode
Dim rngname As Variant
' For Each rngname In ActiveWorkbook.Names '//use for global scope
For Each rngname In ActiveSheet.Names '//use for local scope
If Not Intersect(Selection, Range(rngname)) Is Nothing Then
'..delete the name

' ActiveWorkbook.Names(rngname.Name).Delete '//for global scope
ActiveSheet.Names(rngname.Name).Delete '//for local scope

End If
Next 'rngname

..where this will work if all or part of a named range falls within the
selection.

--
Garry

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