The setting you have in the template looks like the following:
If you highlight the template on the left tree menu (Or Mailbox) this screen will be after selecting "Edit" next to the "File Destinations" field. I am fairly sure yours will be set to "Overwrite existing file", just change it to "Rename New File".
Now if that is right you will need to do so for each mailbox and or template.
But then you will want to stop it from happening again, so go to the "Properties" tab
Then on the left I believe it would be Services/Network Scanning/ Default template and do the same thing here, which will make the new setting the default for everything created at this point forward.