Starkiller was grateful that Leia hadn't pushed. Oh he had no doubt that she had sensed or seen his discomfort. But she wasn't pressing the matter. Which was good. Unless it was Juno pressing the matter, he'd close off. But, she was thanking him for being willing to teach her how to fight with a saber. He'd just have to remember to not be as brutal as Vader had been on him.
"...I've never been Galen Leia. Maybe as a kid before Vader but...being Starkiller, Vader's apprentice is all I've known. It's not really the kind of thing you just can change your name with and forget."
He felt oddly touched though that Leia was giving him a clean slate. "But...thanks." He could try to be Galen here. This was his chance to be the man Juno saw him as. He had to take it. If he didn't, he'd just keep being Vader's puppet.
"Any particular time you want to start dueling, let me know."