Change the link of ‘Howdy’ at the top right

It’s not well documented, but the add_node and add_menu methods of the WP_Admin_Bar class can be used not only to create new menu or nodes, but also to update an existing menu or node.

So i went ahead and tracked down the code that WordPress initially uses to create that item in the admin bar, replicated it, then made adjustments to the Howdy text and used an example link to google. Simply make your own adjustments as appropriate to the example code.

Example code:
Update the user account menu in the admin bar

function wpse_98066_before_admin_bar_render() {

    global $wp_admin_bar;

    if( !method_exists( $wp_admin_bar, 'add_menu' ) )
        return;

    $user_id      = get_current_user_id();
    $current_user = wp_get_current_user();
    $my_url="http://www.google.com";

    if ( ! $user_id )
        return;

    $avatar = get_avatar( $user_id, 16 );
    $howdy  = sprintf( __('Hey, nice to see you again, %1$s'), $current_user->display_name );
    $class  = empty( $avatar ) ? '' : 'with-avatar';

    $wp_admin_bar->add_menu( array(
        'id'        => 'my-account',
        'parent'    => 'top-secondary',
        'title'     => $howdy . $avatar,
        'href'      => $my_url,
        'meta'      => array(
            'class'     => $class,
            'title'     => __('My Account'),
        ),
    ) );
}
add_action( 'wp_before_admin_bar_render', 'wpse_98066_before_admin_bar_render' );

I hope that helps, have fun. 🙂