"So, do you want to join Starfleet and go to Klingon and the other side of the galaxy?"
This quote does not make sense.
So here’s the thing. The Klingon homeworld didn’t have a canonical name until TNG’s Sins of the Father which aired in March of 1990. Of course, NOW everyone knows it’s Qo’noS, but up until then the closest we had was the non-canon “Kitumba” idea from a Phase II script that never happened.
Star Trek VI came out in December of 1991, almost two years later.
So why would Eugene Bowski, a Star Trek fan who liked Star Trek enough to proselytize outside a movie theater not know the name of the Klingon homeworld? It doesn’t make any sense.
As far as I can tell there are only TWO explanations.
EXPLANATION ONE: The first and most likely is that Dana Tofig has MISQUOTED Eugene Bowski and that Eugene Bowski was probably really embarrassed by such a quote and was made fun of by the crew of the Nautilus.
EXPLANATION TWO: Less likely is that Eugene was doing it on purpose. If he was wearing “a snug blue-and-white Federation-approve uniform” then he’d be dressed in the 2271 “Star Trek The Motion Picture” outfit, which look like this:
and maybe, maybe, Eugene was trying to stay in character, somehow reasoning that if the name hadn’t been established in canon by the Motion Picture era, then a character FROM that era would call the planet by a wrong name?? But even so, a fan with this much commitment would probably call it “Kitumba” (from Phase II) or “Kling" and not "Klingon". After all, we don’t call our planet "Human".
IN CONCLUSION: I’m pretty sure Dana misquoted Eugene here and I’m glad that with our modern technology we can right this decades-old wrong:
"So, do you want to join Starfleet and go to Qo’noS and the other side of the galaxy?”
-Eugene Bowski, for real this time