The session.name option in the /etc/php.ini file will contain the name of the session cookie. By default, the name of the session code is PHPSESSID. 

session.name = PHPSESSID

You can change this to some other name, such as SessionCookie. The name should not contain any spaces or special characters.

session.name = SessionCookie

Restart HTTPD, and ensure HTTPD is active and running.

[root@server1 ~]# systemctl restart httpd

The cookie in the browser should now show the updated name.