The terms used in the International Social Security Association’s Social Security Programs Throughout the World books are “half orphan” and “full orphan.”
The website https://www.25project.org/sponsor/faqs/ uses the following terminology:
Paternal Orphan: A child whose father has died.
Maternal Orphan: A child whose mother has died.
Full Orphan / Double Orphan: A child whose parents have both died.
Social Orphan: A child who has lost one or both parents because of abandonment, or relinquishment due to poverty, alcoholism, or imprisonment.
Here an Ngram graph for “double orphan,” “full orphan,” “complete orphan.”
And the use of "complete" in the second example in #2 conceivably goes beyond its technical sense (i.e., lacking both parents)---the next sentence inclines me to read Nicholson's words as using "orphan" both in its literal and figurative senses, i.e., more here in the sense in jeder Hinsicht verwaist than simply Vollwaise.