The Facebook Comments box, unfortunately, requires that a user is logged in using one of the providers they support. The currently support Facebook users, Hotmail, Yahoo and AOL for authentication and comments. Those users don't have to be logged into your Joomla site, but they do have to be logged into one of those providers, which are shown as options when the user is not logged into one of those.
Beyond that, there's no way to let guest/anonymous users comment. Facebook had that ability many years ago but removed it due to abuse. They want some way to track comments by users, mainly so that they can easily detect spammy users.
If you aren't seeing the additional login providers, login to Facebook with an administrator of your Facebook application and then go to your site with a comments box. In the top of the box there should be a "Settings" link. Click that and enable the "Allow other providers" setting (I don't recall the exact name).
Beyond that, you mention Komento. I believe that has the ability to let guest user's comment. There's no way to import Facebook comments into Komento though.
I hope that helps explain, but should you have any other questions or comments, just let us know.
Thanks,
Alex
Migrating with Komento
