∀P∈{X | X lives in Japan} : P is named Sato

using De Morgan's negation rule this is equivalent to

⇔ ∄ P ∈{X | X lives in Japan} : P is not named Sato

Since {X | X lives in Japan} = ∅ is the empty set, such a person P can by definition not exist. Which means, the first statement is true. If no person lives in Japan, that means every person living in Japan is named Sato.