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Check out the wp_cookie_constants() and ms_cookie_constants() functions, to see available cookies.

Test #1

If we want to use the COOKIEHASH constant, then it's to early to hook into muplugins_loaded. We might therefore try the registered_taxonomy hook, but I haven't tested it yet:

add_action( 'registered_taxonomy', function()
{
    if( ! did_action( 'registered_taxonomy' ) && function_exists( 'wpse_cookie_constants' ) )
        wpse_cookie_constants();
});

function wp_cookie_constants()
{
    if( ! defined( 'COOKIEHASH' ) )
        return;
    
    define( 'USER_COOKIE',          'wpse_user_'      . COOKIEHASH );
    define( 'PASS_COOKIE',          'wpse_pass_'      . COOKIEHASH );
    define( 'AUTH_COOKIE',          'wpse_'           . COOKIEHASH ); 
    define( 'SECURE_AUTH_COOKIE',   'wpse_sec_'       . COOKIEHASH );
    define( 'LOGGED_IN_COOKIE',     'wpse_logged_in_' . COOKIEHASH );
    define( 'TEST_COOKIE',          'wpse_test_cookie'             ); 
}

Test #2

Another approach would be to try this in the wp-config.php file (also untested):

if ( !defined( 'COOKIEHASH' ) )
{
    $siteurl = get_site_option( 'siteurl' );
    if ( $siteurl )
        define( 'COOKIEHASH', md5( $siteurl ) );
    else
        define( 'COOKIEHASH', '' );
}
define( 'USER_COOKIE',          'wpse_user_'      . COOKIEHASH );
define( 'PASS_COOKIE',          'wpse_pass_'      . COOKIEHASH );
define( 'AUTH_COOKIE',          'wpse_'           . COOKIEHASH ); 
define( 'SECURE_AUTH_COOKIE',   'wpse_sec_'       . COOKIEHASH );
define( 'LOGGED_IN_COOKIE',     'wpse_logged_in_' . COOKIEHASH );
define( 'TEST_COOKIE',          'wpse_test_cookie'             ); 

But I also wonder, as @PieterGoosen, why you need to change it.