You can get the path via fp.name. Example:
>>> f = open('foo/bar.txt')
>>> f.name
'foo/bar.txt'
You might need os.path.basename if you want only the file name:
>>> import os
>>> f = open('foo/bar.txt')
>>> os.path.basename(f.name)
'bar.txt'
File object docs (for Python 2) here.