The instance name (and instance number) are created when the form is first submitted.
see here: /Documentation/manual/html/form_instance_name.htm
but if you want to use this in all notifications including from the first submission there are a couple of ways you could do this.
1: use the ‘submit and reopen same instance’ such that the form maybe opens and automatically submits and reopens through a new ‘first stage’. In other words before the users are able to actually start to use the form it has already been submitted and of course any existing actions (connections etc) that you are running on the current ‘first stage’ you don’t run, but run them on the new ‘second stage’
2: set up a set field action on the form that runs before you submit, that is replicating how you want to define your form instance name (see step 5 in the above page in the user guide) to a hidden field on your form and then link to that field in the email notification
Assuming you have set up your form already, check these methods out on a simple test form so you can see how they work to see which is more suitable for your overall process