I've seen people write similar things elsewhere, and I agree, but I feel like a lot of people seem to have missed an essential point: the name "Martha" didn't make Batman realize that Superman was "a good guy because he had a mother with the same name," but slowed Batman down enough to realize that the Batman-Superman conflict had been entirely orchestrated by Luthor.
Yes, Bruce was clearly angry at the end of the Zod-Superman fight--and understandably so. But Luthor manipulated him and stoked that anger until it consumed him entirely. So when he was able to take a step back, see that Luthor had manipulated him for almost 2 full years since those events, and rethink Superman's character outside of what Lex had done to manipulate him--at that moment, he was able to realize that Superman was not the enemy.
The name "Martha" was the catalyst. Not the entire cause of his reversal of opinion toward Superman.
That, to me, was both really powerful and plausible, and I applaud the story for that level of sophistication.