I'm thinking about renaming my latest mission "Trembler 4" to something else. It is really a throw away mission that has nothing to do with my on-going plot and was designed solely to show off my city-building skills. I've already got more than 12 reviews. Will renaming it cause any issues (other than those who might be looking for it under its old name)?

should not have any effect at all on the misison/reviews. you have to rename it, save and then instantly republish it for it to take effect.

I suspect all things like reviews are tied to the project ID, not the name.

^^^^
This is indeed the case. Renaming it won't cause you to loose any star rankings or review comments currently associated with it. The worst that will happen is that it goes back into 'review' status and will take another 5 plays to appear again on the 'Community Authored' tab.

Hm, I must try that myself again... I have an unpublished mission and want to make a slight change to its name, but every time I rename it and save, the next time I look it has its old name back.

yep it only works if its published straight after doing it, just a normal name change wont work.