When merging 2 tickets, you can prevent the Email Notification from being sent to Customers that Ticket has been closed. 


While merging Tickets in Freshdesk, there is an option to Add as Private Note, and don't notify the requester, choosing which, the merge will not be notified to the Customers. This has to be enabled in all the tickets that are being merged into one, i.e., the original ticket as well as the ticket(s) to be merged with.