How to change the recipient email address in ticket replies?

While replying to tickets the recipient in the 'To' field will be the original ticket requester by default. To change the recipient, you can change the requester of the ticket and the 'To' field will change as well. If you are looking to reply to a few other users, you can add those recipients in the 'CC' field. 

But, If it's a third party and you are looking to contact them without the knowledge of the requester, you can make use of the 'Forward' option. The forward and the reply to the forward will be added as a private note so the customer will not be aware of the forwarded conversation.