In the movie Memento, is there any mention about how Lenny narrowed the second attacker's name to be John G? In short, how does Lenny know that he's looking for someone with the name John G?
My understanding is that there was no second attacker. Having already killed the man who attacked his wife, with Teddy's help, Leonard invented a second attacker so that he could continue his hunt, as it was the only thing giving his life meaning.
The implication is that Leonard chose the name "John G" to be deliberately vague, to make it easier to find potential targets. IIRC, Teddy specifically calls him out on this during the big reveal, saying something like, "There's a thousand 'John G's out there! Hell, I'm 'John G'!" This ends up being a factor in Leonard choosing Teddy as his next target.