You don't need to add the deleted_at to the dates array, the trait will handle that for you.
I'm not sure what your problem is, I see your model and migration but no code how you use it.
If you use a create/update using a mass assignment you need to add the name field to your $fillable array. Else it will not filled. Maybe is that part of your question.
Did you find the documentation about soft deletes? https://laravel.com/docs/8.x/eloquent#soft-deleting
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