The reviews are satirical parodies on real Star Trek episodes, and one of the things that makes them funny is giving the characters names based more on their actions than what Paramount decided would be good.
If they don't have a nickname yet, it's because I haven't thought of one that I consider funny enough to use. Don't worry, no-one will miss out!
As I'm a big fan of Red Dwarf, you will see a few references here and there. Others may be a little more obscure.
Here is summary of the commonly used ones: