This is not something we can change. Those are Facebook rules, terms, and conditions. The plugin will use the name of the user who authorized the Facebook app.
1. Post to user profile will be posted as the user’s name.
2. Post to all kinds of pages (business, fan, etc..) will be posted as page’s name.
2. Post to groups will be posted as the user’s name. (!) There is no such thing on Facebook as post as “Group’s name”. No one can post like this.