It's a joke. The books are called The Berenstain Bears. Because surnames ending in -stain are extremely rare and surnames ending in -stein are fairly common, a lot of people misremember them as The Berenstein Bears.

This has spawned numerous conspiracy theories about the name changing. There is a group of people who seriously believe they've somehow travelled into a parallel universe where the only difference is that a children's book series is named differently. This theory is often referred to as "the Mandela Effect", which is named after how a lot of people mistakenly remember hearing about Nelson Mandela dying years before he actually did (and yes, these people claim that they've accidentally travelled to a parallel universe where the only difference is that Nelson Mandela lived another 15 years). The theory sounds like a joke, but its proponents take it dead seriously, and they've been known to start flamewars over it.

As such, a lot of people like to make fun of these conspiracy theories by concocting the most ludicrous theories we can think of.