Index: widgets.php
===================================================================
--- widgets.php	(revision 15380)
+++ widgets.php	(working copy)
@@ -545,7 +545,7 @@
 
 	$defaults = array(
 		'name' => sprintf(__('Sidebar %d'), $i ),
-		'id' => "sidebar-$i",
+		'id' => !empty( $args['name'] ) ? 'sidebar-'.sanitize_title_with_dashes( $args['name'] ) : "sidebar-$i",
 		'description' => '',
 		'before_widget' => '<li id="%1$s" class="widget %2$s">',
 		'after_widget' => "</li>\n",