I know that this whole "alternate universe" thing is just for fun, but the real explanation for this is that it's just people misreading things, we've all done it. I used to read "Vaporwave" as "Vaporware", for example (dumb I know).
First off, Stain is very similar to Stein. Stein is a more common name, and people read it wrong. Most people are only barely literate anyway, especially children. Also, everyone pronounced it "Bernstein"; therefore they thought it was spelled that way.
"Play it again, Sam." is not in Casablanca. Darth Vader never said, "Luke, I am your father." Kirk never said, "Beam me up, Scotty". Carl Sagan never said "billions and billions", except to say that he never said it. You thought "Sex and the City" was "Sex AND the City" because "in" is phonetically similar to "and", even though it was always meant to be "and". Human memory is not perfect.