In Levi's case, he works on the assumption that he may not be the only one from his world here, and that the other people may be ones who wish him dead. In that scenario, his name is more than enough, especially considering he's something of a mini celebrity.

"About ten days ago," he confirms. "I know Senku, Randvi and K." He looks at Martin. "And now you." Pause. "And Maddy."

So he may have broken his introduction rule for her because he did let her know his name before meeting her. But it seemed like it might give her some comfort to know who's coming for her, and he couldn't deny her that.

That is... definitely not an extensive list, though.