Could you create a new attribute (or reference list) on the process object named something like "Template ID". Then set this with the name of the template as part of your template - if that makes any sense!!
So for example:
Modify your default incident window and add the attribute created above.
Modify your template(s) and update the attribute with the relevant ID for the template.
Modify you default incident window to hide the template ID attribute.
Then when a ticket is logged using a template you will have a reference of the template that was used.