You'll just need a
for loop to iterate through multiple items (in this case, strings of the paths to your shapefiles) if you wish to perform the same procedure on multiple items.
A basic template:
#Paths to shapefiles
distFc = r"C:\test\example\district.shp"
mandalFc = r"C:\test\example\mandal.shp"
villageFc = r"C:\test\example\village.shp"
#Create list of shapefiles
shapefiles = [distFc, mandalFc, villageFc]
#iterate through each shapefile with a for loop
for shp in shapefiles:
#Create update cursor
with arcpy.da.UpdateCursor (shp, ["DName", "MName", "VName"]) as cursor:
for dName, mName, vName in cursor:
# code goes here