Remembering names is simple enough. It's just data that gets burned into her memory. Just like the very recent memories of her inevitable fate regarding a particular genocidal machine from her own world -- so, for his sake, it is likely knowledge best kept unearthed for now.

"Alan," she repeats with barely a nod. "Well, unless you have any further questions, will leave you to your own devices for now. Am assuming you'd like to contact the gods as soon as possible."

Just a hunch.