Silence fell. Admittedly, Kylo Ren had not anticipated that question. Now, he struggled with how he wanted to answer. He could have feigned not knowing anything further than a name, but that was a lie easily seen through. This Jedi was no fool. So, he gathered up what strength he had from where he lay on the bed and turned to stare Obi-Wan down.
"He was my father."
What did he have to lose? This island was torture. He would never leave. No one knew him. He had no reputation but that which he built. And if this Jedi before him would kill him for his actions...at least he wouldn't have to be here in this awful place any longer.