iterating through all files from a folder

[gonzo620]

You've been a huge help! I just have one last question.

import pathlib

name = input('Enter a name: ')

path = pathlib.Path("./Names")
for entry in path.iterdir():
    if entry.is_file():
        with open(entry,'r') as f:
            for line in f:
                if name in line:
                    name_count = line.count(name)
                    print(name_count)

this program is printing a 1 for every occurrence of 'name'. What I want is to print the total number of occurrences 'name' has throughout all the files. What am I missing?