EDIT:
Here I have registered 2 sidebars in functions.php with names sidebar1 and sidebar2.
$sidebar_args = array(
'name' => __( 'sidebar1', 'theme_text_domain' ),
'id' => 'sidebar-1',
'description' => '',
'class' => '',
'before_widget' => '<li id="%1$s" class="widget %2$s">',
'after_widget' => '</li>',
'before_title' => '<h2 class="widgettitle">',
'after_title' => '</h2>' );
register_sidebar( $sidebar_args );
$sidebar_args_2 = array(
'name' => __( 'sidebar2', 'theme_text_domain' ),
'id' => 'sidebar-2',
'description' => '',
'class' => '',
'before_widget' => '<li id="%1$s" class="widget %2$s">',
'after_widget' => '</li>',
'before_title' => '<h2 class="widgettitle">',
'after_title' => '</h2>' );
register_sidebar( $sidebar_args_2 );
And now retrieving their names on theme’s page like this.
<?php
global $wp_registered_sidebars;
$my_sidebars = $wp_registered_sidebars;
foreach($my_sidebars as $my_sidebar){
echo $my_sidebar['name'];
}
?>