It's easy to forget some of the subtle differences between the Superman of Earth-1 and the Superman of Earth-2. One easy example: Earth-2's is named Kal-L, not Kal-El.
Here's another one most people have forgotten, as Clark Kent-2 has his first meeting with Lana Lang-2:
BATMAN: You were never a god. You were never even a man.
SUPERMAN: You're letting them kill Mary!!
BATMAN: Sorry, I don't know anyone by that name.
He plunges the spear into Superman's chest, killing him.
See? The ridiculous coincidence of their mothers having the same first name was a great plot point, and the only thing that stopped Batman from straight up murdering Superman (not to mention the brilliant screenwriting that set it up so that coincidence works if and only if Superman says "Save Martha" instead "Save my mom" or such...).
Too bad about Earth-2 getting wiped out by Doomsday, though...
From Superman Family #203 (1980)