How to change cookie name

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

We can try this in the wp-config.php file:

// Here we just simulate how it's done in the core
define( 'COOKIEHASH',           md5( 'http://example.tld' )    ); 

// Then we override the cookie names:
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'             );

or using PHP 5.6+ :

// Then we override the cookie names:
const USER_COOKIE        = 'wpse_user_'      . COOKIEHASH;
const PASS_COOKIE        = 'wpse_pass_'      . COOKIEHASH;
const AUTH_COOKIE        = 'wpse_'           . COOKIEHASH;
const SECURE_AUTH_COOKIE = 'wpse_sec_'       . COOKIEHASH;
const LOGGED_IN_COOKIE   = 'wpse_logged_in_' . COOKIEHASH;
const TEST_COOKIE        = 'wpse_test_cookie';

where we must adjust the site url http://example.tld to our needs.

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