You could add a Javascript check in the default.php, which we can help you do as well, but that won't prevent someone from proceeding with a space in their name anyways. You can make the following change and you should be good to go though:
In /components/com_jfbconnect/libraries/facebook.php, at line ~34, you'll see where we fetch the username that was entered. After that, put:
if (strpos($username, " "))
{
$app->enqueueMessage("No spaces in username!!");
$app->redirect(JRoute::_('index.php?com_jfbconnect&view=loginregister', false));
}
Let us know if that works for you or if you run into other issues, and good luck!