This is something that I've been wondering about, how does L deduce that Kira needs a name? Surely all the victims he investigated had their name and face, but how can he figure that he needs both? The stunt on tv with Lind L. Tailor only proved that Kira can't kill anyone, and there are certain criteria. I'm not sure how that concludes that he needs both name and face.
Edit: To clarify, here's how I look at it. L analyzes all the victims of the Kira killings and noticed that what was broadcast about the criminals was their face and their name. How does he conclude that Kira needs both? Why not just a face? When Kira kills Lind L. Tailor, that only validates that Kira has the ability to kill people, to which L himself even says "I couldn't believe it until I saw it, but it appears you can kill without being there in person." When Kira subsequently is unable to kill L, L can then deduce that there are people Kira can't kill. However he concludes Kira needs both name and face, which I don't understand. To me, at that point 3 conclusions are viable: Kira needs a name AND a face. Kira needs just a name. Kira needs just a face.