Index: src/wp-includes/theme.php
===================================================================
--- src/wp-includes/theme.php	(revision 51925)
+++ src/wp-includes/theme.php	(working copy)
@@ -1208,6 +1208,13 @@
 	$width  = absint( $header->width );
 	$height = absint( $header->height );
 
+	// Use alternative text assigned to the image, if available. Otherwise, leave it empty.
+	if ( ! empty( $header->attachment_id ) && ! empty( get_post_meta( $header->attachment_id, '_wp_attachment_image_alt', true ) ) ) {
+		$alt = get_post_meta( $header->attachment_id, '_wp_attachment_image_alt', true );
+	} else {
+		$alt = '';
+	}
+
 	$attr = wp_parse_args(
 		$attr,
 		array(
@@ -1214,7 +1221,7 @@
 			'src'    => $header->url,
 			'width'  => $width,
 			'height' => $height,
-			'alt'    => get_bloginfo( 'name' ),
+			'alt'    => $alt,
 		)
 	);