This actually has nothing to do with the plugin. This is the setting of your page. Please go to your Facebook Page, click “Edit Page”->”Update Info”, click “Your settings” from the left menu -> Posting Preferences, check checkbox “Always comment and post on your page as [Page Name], even when using Facebook as [Your name].”
UPDATE: (Sept, 2013) It looks like for some users Facebook has removed “Always comment and post on your page as [Page Name], even when using Facebook as [Your name].” checkbox from the settings and left users hanging at some uncertainty. We are currently investigating this issue and trying to find out the way to specify what account should be used for posting.
UPDATE: (Dec, 2013) The person who authorizes the plugin must be an admin of the page at the authorization time. Post will appear as page name in this case. If this doesn’t work, try to re-authorize or create a new Facebook app.