Notification on assigning a test case

I wish that were the case, sadly not.

The way I currently workaround that issue is to create a report specific to each tester showing  their outstanding tests.  As the report is dynamic, if a test is assigned to them they will see it in the list.  Far from perfect but there are limited options using the UI for this.  It might be possible to do something more sophisticated with the API and some applied logic but I've not had time to look into such a solution.