It’s possible to do, but would take hacking up the theme. One convention I’ve seen is to create a user with a generic name, like Guest, or the name of your site.
If you would still like to hack away. Then put a condition around the line\s in the template that displays the author like so:
<?php if (get_the_author() != 'none') : ?>
<?php the_author(); ?>
<?php endif; ?>
or alternately, the shorthand…
<?php echo (get_the_author() != 'none') ? get_the_author() : ''; ?>
Then you define an author named ‘none’.
The post will only display the author’s name if the name isn’t ‘none’.