Change the name of the root name of an already built WordPress theme

You should never use <link> tags for stylesheets. Always use the proper API functions:

Better practice Example:

function wpse57423_register_stylesheets()
{
    wp_enqueue_style( 
        "themes_main_stylesheet'
        get_stylesheet_directory_uri()."/style.css"
        array() // Use this array if you've deps that need to load before your stylesheet
        filemtime( get_stylesheet_directory()."/style.css" )
    );
}
function wpse57423_enqueue_stylesheets()
{
    wp_enqueue_style( 'themes_main_stylesheet' );
}
// Add to public page
add_action( 'wp_enqueue_scripts', 'wpse57423_register_stylesheets' );
add_action( 'wp_enqueue_scripts', 'wpse57423_enqueue_stylesheets' );
// Add to login
add_action( 'login_enqueue_scripts', 'wpse57423_register_stylesheets' );
add_action( 'login_enqueue_scripts', 'wpse57423_enqueue_stylesheets' );
// Add to admin UI/backend
add_action( 'admin_enqueue_scripts', 'wpse57423_register_stylesheets' );
add_action( 'admin_enqueue_scripts', 'wpse57423_enqueue_stylesheets' );

^{Please note that the login page needs specific treatment. Refer to this answer if you need to handle it.}

This allows to

• enqueue/register styles only where you need them and don’t load them everywhere
• child themes the possibility to override your styles with adding a stylesheet with a) the same name in b) the same position in their folder
• deregistering stylesheets in child themes
• unhooking the functions