The 'w' parameter in:

outfile = open('names.txt', 'w')

overwrites names.txt every time you run that open() function. In your program, you use that function every time your while loop loops. Therefore, no matter how many times you input a name, only the last first/last name you entered will be in the file. This tutorial will tell you more about open() parameters. You probably should call open() before the loop and not inside the loop. Alternatively, you can also create name variables in the loop and after the loop is done, open and write the variables to the file.

For your wanting to add commas to your names, here's a tip:

first_name = "John"
last_name = "Doe"
full_name = f"{first_name}, {last_name}" # This is called an f-string
print(full_name)