If you want to make it less cliche, then don't give it a name that is "The (Noun)". Look the names of hospitals, schools, and mental health centres, and see what you can come up with.
The Sanctum seems appropriate. I know it's hardly any different in appearance but if the definition of "sanctum" is "a place where people are excluded from" it can inversely be interpreted as a place where people are isolated in. Also, I know it appears as a synonym in the thesaurus but by definition "sanctum" is quite distinct from "sanctuary". It also has a religious connotation so you could experiment with some symbolism if you're not afraid of controversy.
http://www.fantasynamegenerators.com/ is my go-to for just about any name. Even if it doesn't do descriptions well, it can name practically anything or give you ideas to figure them out yourself. EDIT:: You could always go with something simple like Desolace, or Desolation Hold, or something like that. Is it a fantasy dystopia, or a set-in-a-world-that-could-be-real dystopia?
How about just giving it it's own name like you would a character. The most famous prisons that I know don't have names like "The Sanctuary." They're called things like Belmarsh, and Buckley Hall. Think about Alcatraz. The prison isn't iconic because of the name. The name is iconic because of the prison. I'm always impressed when I'm introduced to new names and titles. For example in Star Wars , they could have called Obi Wan a knight of the realm, or protector of the peace, but they just made up a new word and called him a Jedi. That's so much more badass.
I agree with @halisme and @cockneyjay that it makes sense to name it after a place, more like the way real prisons and institutions tend to be named. You can even put a subtle symbolic reference in the etymology of the place name. But if there are multiple "sanctuaries", you would almost definitely hear them referred to by location like this. You should think about how it would realistically be referred to in-world. Maybe there is a fancy euphemistic official name, but most people refer to it by the place name or a catchy abbreviation. Maybe the locals casually refer to it using a shorthand like "the center", which could give you that noun effect. Simplicity can be more powerful than contrived grandiosity.
Always this. Doesn't matter what you're naming; just because it's got a big name, doesn't mean it's worth anything. Sometimes, a smaller, simpler name can resonate better.
You want something that feels faintly villainous while being difficult to pinpoint exactly why. Someone above mentioned: 'Fellwater' As an example, it's got the vampiric association of 'fell' and the mundane 'water'. As a name, it's quick to say and could legitimately be used by crooks, unlike some of the very long suggestions in here.
Thank you for all the responses! I changed the name a while ago, with inspiration from one of the ideas posted here. I went with "DRAIN," for Distortion Relocation Alliance of Integrated Networks. The Distortion was the government's name for the dystopian event that changed the nature of the earth, and DRAINs are where the government rounded people up into the centers after. The government calls the centers "Networks" or 'The Alliance," but everyone else uses the acronym and jokes about what depressing drains the places are. Thank you everyone! Sorry for not returning to this thread sooner.
Hi, please do not try to create an acronym that is a recognisable word, it always sounds false. Detention & Rehabilitation of Antisocial Institutional ... I can't make it work...
Umbra > means shadow on latin, sounds simple and people won't know what is that exactly, but it'll sound cool
This really sounds interesting to me. Perhaps the official name can be the name of the facilitator, and the number is the year they took charge. You could also consider having an "official name" as well as a nick name. So the inmates of a correctional facilitate could call the place the hive, or the grind, or something like that.
I agree with Big Soft Moose. I immediately got the "1984 irony" when I read it. I wouldn't go for anything ironic like that, NOR would I use something standard like "Correctional Facility". Instead, what I would do is go historical. Give a kind of nod to a famous prison, like Alcatraz or the Bastille or the Tower of London or something. Use a little wordplay to rename a famous prison? OR, what you could do is name it something where the name implies that it's impossible to escape from, like "Black Hole" or "The End" or something. Ok, those are bad examples but you get my point. That's what I'd do anyway. I love dystopian novels. 1984 and Brave New World being the obvious top-shelf picks for me.
The Penitentiary, The Rock, The Correctional Facility, The Penal Institution. Then you could just put the name of your country before.