no need to use a custom table, use an option, and the add_attachment hook:
function wpa59168_rename_attachment( $post_ID ) {
$post = get_post( $post_ID );
$file = get_attached_file( $post_ID );
$path = pathinfo( $file );
$count = get_option( 'wpa59168_counter', 1 );
// change to $new_name = $count; if you want just the count as filename
$new_name = $path['filename'] . '_' . $count;
$new_file = $path['dirname'] . '/' . $new_name . '.' . $path['extension'];
rename( $file, $new_file );
update_attached_file( $post_ID, $new_file );
update_option( 'wpa59168_counter', $count + 1 );
}
add_action( 'add_attachment', 'wpa59168_rename_attachment' );