Where I lived, everyone pronounced it BerenSTEIN instead of BerenSTAIN, which was probably common everywhere in the US since nobody had ever heard of anyone with the name BerenSTAIN before, but were familiar with BerenSTEIN and how to pronounce it. And if it was commonly pronounced that way, it would make sense that people would think it was spelled that way.
Also, the Berenstain Bears logos on the books were all in cursive. Most kids read those books before they learned how to read cursive writing. Had the spelling been in regular print, the name BerenSTAIN would be more firmly etched into people's minds. The books did have a "by Jan and Mike Berenstain" on them in regular print, but it was smaller and well away from the title of the book. Besides, Berenstain or even Berenstein is one of those longer, more difficult words for 5 year olds to understand, so it's unlikely they paid much attention to it anyway.
I can come up with possible explanations for stuff all day. I will admit that I also didn't realize it was BerenSTAIN and always thought it was BerenSTEIN, but I'm willing to take accountability for my terrible memory instead of blaming it on parallel universes merging