$cat_id = $this->category;
$query = $DB->get_record_sql('select name from mdl_question_categories where id="' . $cat_id . '"');
print($query->name);
I discovered the answer and am documenting it here in case someone else needs it. It seems that the category id is stored in the category field. You can get the category using:
Thanks for posting Charlie, that should work but you should consider something like
$DB->get_record('question_categories',['id'=>$cat_id)
Then it will work if someone has a prefix other than mdl.
See
https://docs.moodle.org/dev/Data_manipulation_API#Main_info
I suspect most people most of the time leave the default mdl_ but it is nice to cover unusual situations.
Thanks Marcus,
It's good to see an elegant approach.