Charles does pull back finally from the second kiss, not wanting her false sympathy. His own features close off, knowing he's going to have to take whatever comes next. "Keep it in mind. Even after this, no matter which way it goes," Meaning even if she kills him or breaks him, "you could do some very good things in this world if you wanted to."
He has no intention of giving her a safe word, hoping instead that she'll either change her mind or go too far. Both would accomplish not giving Stryker what he wants. "...I can give you my name...if you give me yours." He does want to remember her, in case beyond all hope they make it out of here, he wants to try and get her out as well.