add post format

add_theme_support( 'post-formats', array( 'aside', 'gallery' ) );
would certainly work.

http://codex.wordpress.org/Post_Formats

I think different names are not supported however you can do it like this.

add_filter( 'esc_html', 'comi_rename_post_formats' );
function comi_rename_post_formats( $safe_text ) {
    if ( $safe_text == 'Quote' )
        return 'Game';
    elseif ( $safe_text == 'Link' )
        return 'Story';
    elseif ( $safe_text == 'Image' )
        return 'Edge Article';

    return $safe_text;
}

//rename Aside in posts list table

add_action('admin_head', 'comi_live_rename_formats');
function comi_live_rename_formats() {
    global $current_screen;

    if ( $current_screen->id == 'edit-post' ) { ?>
        <script type="text/javascript">
        jQuery('document').ready(function() {

            jQuery("span.post-state-format").each(function() {
                if ( jQuery(this).text() == "Quote" )
                    jQuery(this).text("Game");
                else if( jQuery(this).text() == "Link" )
                    jQuery(this).text("Story");
                else if( jQuery(this).text() == "Image" )
                    jQuery(this).text("Edge Article");
            });

        });
        </script>
<?php }
}