Yeah, it would have been really upsetting! One of the great things about the show was that they didn't have any ginormous names making appearances and taking the watcher out of the world they'd created. I mean SMG was very well known by some when the show started but she wasn't a mega star so it wasn't difficult to accept her in her role. John Ritter was sort of an exception to that but I don't think he was nearly as famous when "Ted" aired, and in any case, not as much as Britney.
Just the characters' names, I think, are a way for us easily get lost in the Sunnydale world. Uncommon names like "Buffy," "Willow," "Cordelia," "Angel," etc make it so that we don't think about for example, "the Buffy I went to school with" and can allow ourselves to concentrate on what's in front of us.