I pick a language or culture, and pick names that sound like they're from that culture/language/flavor/whatever.
Like my fantasy nation has an ancient Greek vibe to it, so I've named the provinces and plot-relevant cities/villages after Greek deities. My current protagonist's village is named Carmanacles, after a lesser Greek personification of fishing. 'Cause it's a fishing village and stuff.
"Jack, you have debauched my sloth."I have trouble choosing names sometimes too. I've resorted to switching syllables of a word (chaos > oscha), using a portmanteau (flower elves > felves), and just using a simple pair of words (armor plant). I've even gotten the name for my spiders that burn their prey alive so they can eat the ashes by using a random generator from Seventh Sanctum
and combining an interesting result from it with one of the names of a group of Japanese spiders (golden silk orb weaver) to get the name blazesilk weaver. It helped that I had already planned for my fire affinity spiders to be descended from golden silk orb weavers.
The best names in my opinion, are ones that tell you something about the thing that has the name. If the name can help you identify the thing (rattle snake comes to mind), then it's a good enough name. If it was named after someone, that's OK too. If it tells you why the heck you should avoid it at all costs, then it's a good name.
You don't have to be all fancy and come up with a new word from scratch to use as the name for the new thing. You don't have to abuse apostrophes. You don't have to choose a unique collection of syllables that no one has ever heard together.
If you are really having trouble naming something, then write a sentence that describes it. It could be a description of its appearance, its behavior, or even its origin. Then, start reducing the number of words in that sentence. You can take a word out, or replace two or more words with a single word. Don't be afraid of making up words. Keep this up until you have one or two words which you will use as the name.
Also, what level of cheesiness are you trying to avoid? Because I'm sure that there might be plenty of things here in the real world that have names just as cheesy, if not cheesier. Heck, "Christian" is treated as a normal name to give to a child, and no one seems to think that much about how the child's been named after a religion.

How do you choose names for places and tribes? I totally suck at naming. How do y'all manage?
I'm designing a campaign setting, and everything else flows smoothly, but naming is a pain in the ass.
Any name I can think of has either been picked before or sounds awfully cheesy.
You exist because we allow it and you will end because we demand it.