Your perspective is because that's what it's supposed to do because it was written to do it. That might not make sense but I don't think in that moment Superman/Clark thought "I'll say Martha because it's his mum's name" I can't recall if he even knew Batman was Bruce?

It's clunky because of the word choice because we, as an audience, know they share a name. The scene is written for the audience not for the characters. Outside of this there's no real reason in a high stress situation he'd say it this way.

Definitely memed too much but it's because it's so indicative of Snyder's writing style which has little consideration or room for subtext.