“Every person in Japan will be called Sato.”

In formal logic, this is equivalent to
“There is no person in Japan not called Sato.”

Since there are no people, no one is not called Sato, and therefore every person is called Sato. Every person is also called Steve. Or Klaus.

Edit: once you take the second part of the headline about the marriage law into account you’re right, my bad ^-

For one, there is no legal requirement that a Japanese partner take the name of their foreign spouse (in fact, it’s basically the exception to the rule that all married couples must have the same surname).