Index: src/wp-includes/class-wp-customize-control.php
===================================================================
--- src/wp-includes/class-wp-customize-control.php	(revision 32884)
+++ src/wp-includes/class-wp-customize-control.php	(working copy)
@@ -103,6 +103,12 @@
 	public $input_attrs = array();
 
 	/**
+	 * @access public
+	 * @var string
+	 */
+	public $label_text_class = '';
+
+	/**
 	 * @deprecated It is better to just call the json() method
 	 * @access public
 	 * @var array
@@ -447,7 +453,7 @@
 				?>
 				<label>
 					<?php if ( ! empty( $this->label ) ) : ?>
-						<span class="customize-control-title"><?php echo esc_html( $this->label ); ?></span>
+						<span class="customize-control-title <?php echo $this->label_text_class; ?>"><?php echo esc_html( $this->label ); ?></span>
 					<?php endif;
 					if ( ! empty( $this->description ) ) : ?>
 						<span class="description customize-control-description"><?php echo $this->description; ?></span>
@@ -466,7 +472,7 @@
 				?>
 				<label>
 					<?php if ( ! empty( $this->label ) ) : ?>
-						<span class="customize-control-title"><?php echo esc_html( $this->label ); ?></span>
+						<span class="customize-control-title <?php echo $this->label_text_class; ?>"><?php echo esc_html( $this->label ); ?></span>
 					<?php endif;
 					if ( ! empty( $this->description ) ) : ?>
 						<span class="description customize-control-description"><?php echo $this->description; ?></span>
@@ -499,7 +505,7 @@
 				?>
 				<label>
 					<?php if ( ! empty( $this->label ) ) : ?>
-						<span class="customize-control-title"><?php echo esc_html( $this->label ); ?></span>
+						<span class="customize-control-title <?php echo $this->label_text_class; ?>"><?php echo esc_html( $this->label ); ?></span>
 					<?php endif;
 					if ( ! empty( $this->description ) ) : ?>
 						<span class="description customize-control-description"><?php echo $this->description; ?></span>
@@ -1748,6 +1754,7 @@
 	protected function content_template() {
 		?>
 		<label>
+			<span class="screen-reader-text"><?php _e( 'Menu name' ); ?></span>
 			<input type="text" class="menu-name-field live-update-section-title" />
 		</label>
 		<?php
Index: src/wp-includes/class-wp-customize-nav-menus.php
===================================================================
--- src/wp-includes/class-wp-customize-nav-menus.php	(revision 32884)
+++ src/wp-includes/class-wp-customize-nav-menus.php	(working copy)
@@ -485,7 +485,7 @@
 		) );
 
 		$this->manager->add_control( 'new_menu_name', array(
-			'label'       => '',
+			'label'       => __( 'New menu name' ),
 			'section'     => 'add_menu',
 			'type'        => 'text',
 			'input_attrs' => array(
@@ -492,6 +492,7 @@
 				'class'       => 'menu-name-field',
 				'placeholder' => __( 'New menu name' ),
 			),
+			'label_text_class' => 'screen-reader-text',
 		) );
 
 		$this->manager->add_setting( 'create_new_menu', array(