You could try Survey instead of Discussion.
The issue you will still face is that, in Instructure Canvas, a survey cannot be set to both graded and anonymous at the same time.
If you want to encourage participation but maintain anonymity, you could create an anonymous ungraded survey.
Using the Essay question type the student experience will be the same as the discussion except that they won’t see their peer’s comments.
You will be able to see if students have participated or not, but you will not have visibility of which response was from which student.
You can then provide participation points manually based on the participation list.