Since Berkeley introduced Geniac first before he came up with Brainiac, it seems pretty clear to me that he wanted people to think of ENIAC. He was selling a computer toy, so taking Genius and putting it together with ENIAC gives that suggestion. And if he was thinking along those lines, then Brainiac follows as the same sort of thing.

Since Mort and Otto were teen science fiction nerds in the 1930s, in the Bronx--with Otto becoming a science fiction writer (later comic book writer) and Mort being first his agent (along with Julie) and then his editor, at Standard Magazines (publishers of science fiction stories) and then at DC--it seems to me they made it their business to follow what was going on with science. So they would have known about ENIAC, BINAC and UNIVAC.

The Jimmy Olsen story has a computer-robot called "Brainiac." So it seems pretty clear to me that they were thinking of the super-computers when they came up with this name. But I expect they also realized that it rhymed with "maniac." And it was just one small step from that to calling their alien genius "Brainiac." But the computer came first.