Copy files to same directory with another name

I need to copy all html files inside the same directory with another name and I need to navigate all directories inside the source directory.

Here is my code so far,

import os
import shutil
os.chdir('/') 

dir_src = ("/home/winpc/test/copy/")

for filename in os.listdir(dir_src):
    if filename.endswith('.html'):
        shutil.copy( dir_src + filename, dir_src)
    print(filename)