If you kept the same names of the original Star Trek world then it would breech the fanfic rule. However, if they are different character that just somewhat resembled the original character then it's fine.
Ah thanks, the crew, ship(name/class/design), and all that was going to be unique, originally some terms and design principals would overlap, like warp drives(though this is a more general term now), phasers, etc. I could change things though to make it be more unique. It's a bit wonky when you get into some Sci-Fi names as they're based on real scientific terms. There's also things like "starship" - it's a Trek term, but it's also used in other things, like "Starship Troopers" and Elon Musk's "Starship." But uhm, I'm more interested in just participating even if I can't win.
Ugh idk, I guess we'll see how it goes and if you need me to change something I will. I could try going a bit more satire route, like how Spaceballs is to Star Wars for example, close, but not. I'll see what happens, thank you for the input!