There are some cool desert names right here on our own Planet Earth that could be effective:
Monument Valley
Tablelands
The Arches
Slaughter Canyon (named for John Slaughter, not some sort of catastrophe, but no reason it couldn't work the other way in-game

)
Death Valley (c'mon, that one's just, uh, dying, to be used. I pun in peace)
Redrocks
White Sands (a massive expanse of gypsum dunes in southern New Mexico)
The Salt Flats
The Badlands
There's an alpine desert mountain range in northern New Mexico called the Sangre de Cristo mountains, which translates from the Spanish as "Blood of Christ" mountains (not trying to get into a religious discussion). The name comes from the color of the rock when the setting sun strikes it, so that the mountains seem bright red (it was named by the Spaniards when they had control of the territory in the 16th and 17th centuries). So you could always do something with a feature like that, e.g.:
The Blood Tower (named for the sandstone used to build it, and how it looks when the setting sun strikes it . . . and maybe also for what happens inside, etc.)
Also, you could think about certain desert features in other ways: canyons are just old riverbeds that may or may not have water in them, so one canyon, or wash, or gulch, or arroyo, or wadi, or similar feature might be known as The Dead River (since it's no longer there, so to speak).
There are plenty of great cactus varieties, like Spanish Daggers, and Tumbleweeds, which have good, evocative names.
Certain phenomena could also lend there names: The Simoon Flats, for example. Another one: in the Chihuahua and Sonora desert regions of the southwestern U.S., rain is (obviously) very infrequent. In the Chihuahua desert, there's a large amount of
caliche underneath the initial sand/soil layers (
caliche is a flat bedrock that is fairly non-porous, for natural stone, and it's a real pain-in-the-patuckus to dig through, usually requiring heavy machinery).
Caliche is one reason why it's hard to grow much in the desert areas, unless it's really close to water, 'cause once you dig down a certain distance, you hit impassable stone. Anyway, when it rains, once the sand/soil gets saturated, the water builds up against the
caliche and it doesn't have anywhere to seep, so it supersaturates and becomes standing water or a flash flood.