This is a subject of intense debate online! Like a lot of people, I definitely thought it was Beren*stein* Bears when I was growing up:
http://mandelaeffect.com/berenstein-or-berenstain-bears

But everywhere I look, it's clearly spelled Berenstain! Here's the theme song, which is really clear about how to spell and say it:

I guess I just misread it as a kid! How about you: do you say Berenstein or Berenstain Bears?