I am providing a scripted alternative either in the interactive window or as a stand alone script.
layer = "YOURLAYERNAME" #interactive window in quote, standalone script needs path
arcpy.AddField_management(layer, "Same", "TEXT")
rows = arcpy.UpdateCursor(layer)
for row in rows:
if str(row.getValue("POLYGON_NM)) == str(row.getValue("NAMING"):
row.Same = "Yes"
Then you can select by attributes or do a definition query to look for duplicated municipalities.
The cstr() isn't necessary, but I am used to dealing with integer fields when comparing so it is habit.
After I thought about this a while
I thought there may be a more fun way of doing this. One where you didn't need another column to house the selected features but just keep appending each feature to the current selection.
layer = "YOURLAYERNAME"
arcpy.SelectLayerByAttribute_management(layer, "CLEAR_SELECTION") #clear selection if present
rows = arcpy.SearchCursor(layer) #no need for update cursor so we can use search
for row in rows:
if row.getValue("POLYGON_NM) == row.getValue("NAMING"): #find those in common
arcpy.SelectLayerByAttribute_management(layer, "ADD_TO_SELECTION", ' "FID" = \'' + row.getValue("FID") + '\'') #take this feature's FID (assuming it is there or use some other unique identifier and add it to selected features. If none are selected, it creates a new selection.
This should create a new selection for you. I am assuming the shapefile has a FID or some other unique identifier. I haven't tested this, and I pieced some of it together from some ArcMap documentation. I probably messed up the quotations around the WHERE clause part, but that is where the fun of debugging comes in on your part.
Read through the arcpy parts of these to verify me and/or improve it:
Select Layer By Attribute (Data Management)