It has never been Berenstein. My sister could never keep it straight when we were kids and I used to make fun of her about it, in the same way that I more recently had Mrs Verc confused about whether it was Kirk Herbstreit or Herb Kirkstreet.
"Stein" is just a far more common suffix in names. So everyone assumed it was "stein" and pronounced it as "stein" because their brains just assumed that's what it was.
It's the same thing with the Monopoly guy. Mr Peanut wore a monocle and the Penguin wore a monocle and Scrooge McDuck wore little glasses that looked like a monocle (I thought it was a monocle until I just looked); the monocle-with-top-hat is usually just part of a trope that we automatically sort the Monopoly guy into even though he didn't actually have one.