If I understand it correclty, her father's name would be Jon.
If she had a brother, his last name would be Jonson.
The icelandic normally don't use a family last name if I understand it correctly but rather a patronym.
One of Sweden's most (in)famous criminals, Clark Olofsson, has died. He was involved in the incident that lead to the term Stockholm syndrome being coined.
https://en.m.wikipedia.org/wiki/Stockholm_syndrome