How do I remove ‘Home’ from homepage title?

You can add a check to see if the current page is the home page, and if so skip adding the page title. This would make the final code look like this:

<title><?php

global $page, $paged;

// Add the page title if not the front page
if ( is_front_page() ) {
        wp_title( '|', true, 'right' );
}

// Add the blog name.
bloginfo( 'name' );

// Add the blog description for the home/front page.
$site_description = get_bloginfo( 'description', 'display' );
if ( $site_description && ( is_home() || is_front_page() ) )
        echo " | $site_description";

// Add a page number if necessary:
if ( $paged >= 2 || $page >= 2 )
        echo ' | ' . sprintf( __( 'Page %s', 'twentyeleven' ), max( $paged, $page ) );

?></title>

---

However, the best thing to do would be to use this code in header.php:

<title><?php wp_title( '|', true, 'right' ); ?></title>

And then filter the title using this code in functions.php:

function wpse_132052_wp_title( $title, $sep ) {
    global $paged, $page;

    // Add the blog name
    $title .= get_bloginfo( 'name' );

    // Use the site name and description for the home/front page
    if ( is_home() || is_front_page() ) {
        $title = get_bloginfo( 'name' );

        // Add the site description for the home/front page.
        $site_description = get_bloginfo( 'description', 'display' );
        if ( $site_description && (  ) ) {
                $title = "$title $sep $site_description";
        }
    }

    // Add a page number if necessary:
    if ( $paged >= 2 || $page >= 2  ) {
        echo ' | ' . sprintf( __( 'Page %s', 'twentyeleven' ), max( $paged, $page ) );
    }

    return $title;

}
add_filter( 'wp_title', 'wpse_132052_wp_title', 10, 2 );