So I've been working on my own campaign setting (its taking a lot of work and I'm proud of the effort), and a particular region I've been working on is part of a larger subdivided mountain chain. In world the people refer to it as the "Dire Mountains". But they only call it that because the mountains themselves lie west of the "Dire Wood". As it's currently written there's nothing of interest to make the mountains "dire". No races live there habitually and no one has really explored the region, it's just there.

Superstition can drive a lot of what a people believe and referring to this mountain range as the "Dire Mountains" for hundreds of years will definitely make people believe theirs spooky stuff there and keep your average person away. But these are the things a lot of adventurers will make beelines toward. The name itself evokes a sense of adventure and dread. But there's just nothing there. No evil necromancers, no demonic cults, to barbaric tribes, I don't have a single thing set to be there. And to be honest, I'm kind of out of ideas.

I don't really know what to put there that the adventurers won't steamroll over. In world no ones settled the entire range, partly out of superstition, partly out of lack of necessity. What can I put in this region to make the place seem like it lives up to it's name?

A curse?

Make the mountains themselves the obstacle.

I'm pulling this from Caradhras the Cruel (from the novel, not the movie). The mountain pass living up to its reputation is what made them rethink the direction they were going - not a Wizard far to the South. Gimli blamed the mountain on an old superstition.

Yetis. Frost giants. Werebears. Also, expanding on the curse, it could be because there is a magic weapon (s) on the summit. Also by having lots of snowstorms, like in lord of the rings, it provides lots atmosphere and skill challenges.

Dangerous animals. Polar bears, crag cats, dire wolves. 

One of the mountains is an earth elemental that carved out the entire range? The Wandering Mountain.

I would suggest though that you don’t need to build up every single area with every little detail immediately. 

A dragon worshipping society lives in the mountains.  Dragonborn, kobold, fire newts and maybe more.  Maybe evil maybe not, but highly protective of their dragons that adventurers keep trying to heroically  slay.  

Alternatively the mountain range is fairly new addition geologically speaking and was created during the final battles of an ancient war.  Huge magical battles that released dangerous energy that literally caused the mountains to appear, created volcanoes etc.  Could be ancient undead haunt the mountains or twisted aberrations created from the wild magic.  Weather could be sporadic and capricious, changing swiftly (truly like most mountain weather systems) and deadly at the drop of a hat.  One minute it is sunny and thirty minutes later tornadoes are forming in the mountain valleys.

Or both, the dragon worshippers are in constant struggle with the creatures that inhabit the range just trying to hold their own against constant clashes with the creatures from the area, and surviving the tumultuous weather.

More LotR-inspired: Haunted. Extremely haunted. City of the Dead haunted.

The next question is why would people still dare to go through mountains that were actually dire. Reputations come from somewhere.

First of all, the look. It shouldn't appear like any old mountain range. Imagine strange rock formations, curving arches and twisted spires, jagged peaks and deep cracks. It's not a pleasant place to traverse. And then there's the inhabitants. I liked the idea of one mountain, at least, being a massive elemental, whether it be alive and sleeping, or dead. Perhaps it was once a family of beached zaratans? Anyways, the creatures that inhabit it now could vary widely, from xorns and geonids living in the caves, to yetis and frost giants living on its frosty peaks, to some nasty animals prowling the area. Perhaps, for some reason, all the animals in the area are giant, or rather... Dire? Then it would certainly live up to its name.

Treat it like real mountains the danger comes from the envirionment. 

Difficult terrain, rock slides, lack of resources. You dont worry about the wolves you worry about dehydration, starvation, passing out due to altitude sickness. Force them to carry a fatigued teammate which leads the others closer to levels of exhaustion...then you throw an encounter at them. 

Add some treasures, a forgotten tribe of people who'd been forced off their land making local settlers actually the bad guys, etc...

I have a feeling whatever you choose it'll be great. Just make sure you enjoy it as much as the players.

I think I'll go with kind of a Monster Hunter/Ikoria vibe. I've been drawing a bit of inspiration from a bunch of sources and I feel just having a region with unbelievably dangerous creatures would make for an interesting locale.

Furry shaggy version of dinosaurs please, unless there are like jungle valleys...  lots of big monster hunters critters like wyvern sounds like it cod be lots of terrifying fun.  Remhoraz and other big snow critters to ruin a travelers day.