"Yeah, just visiting," he's... technically... not lying. He is just visiting. Just for an extended stay. It's fine. This is fine. "I'm not from here, I usually live in Tokyo."

But, also, if she's putting her trust in him, shouldn't he at least give her his name?

"You can call me Tamaki."

She can give him her name if she feels like it, but he won't press her for it.