A script that uses the arcpy site-package to read the filename of a feature class, create a field called Name and writes the filename as an attribute in the newly created field.

FilenameAsAttribute.py

"""
A script that uses the arcpy site-package to read the filename
of a feature class, create a field called Name and wirites the 
filename as an attribute in the newly create filed. 
"""

import arcpy
from arcpy import env

arcpy.env.workspace = "SOME/PATH" 

datasets = arcpy.ListFeatureClasses()

for shape in datasets:
    field = "Name"
    expression = str(shape[:-17])
    expression = '"' + expression + '"'
    arcpy.AddField_management(shape, field, "TEXT")
    arcpy.CalculateField_management(shape, field, expression, "VB")
    print "Done with " + shape[:-4]

print "Done"