Giving my language sensibility check where I can.
Unintended meanings are kept to the most likely hits, theres too many names for me to do a full combinatorial analysis, but as we're a political figure you have to assume that some of these will be deliberately used by us, and some of these would be deliberately used to mock/attack us.
A few bad meanings can be ignored, unless they're too on the nose.
[] Tianji
Intended meaning: 天际 - Heaven's Edge
Implications are xenophobic - the Empire being Heaven, and the settlement being at the end of what could be considered Celestial. Its not what we intend obviously, but its what the ImpCons are reading from it.
Unintended meanings:
-Paddy Chicken - A colloquial term for frog meat. This is going to be what most people who actually speak chinese are going to be getting from the name.
-Heaven's Secrets - Half of a saying, that Heaven's Secrets cannot be revealed(or you will be punished).
[] Yunhai
Intended meaning: 云海 - Cloud Sea
This is purely descriptive, we're up in the mountains, and we are deliberately generating a sea of clouds.
Unintended meanings: Relatively few here,most requiring a deliberate stretch.
-Yun(Cloud) can also be Luck(neither good nor bad, just random) on a different tone, Transport, or Dizzy on yet another.
-Hai(Sea) can be Child on a different tone.
-So it could be Child of the Clouds or Sea of Luck with deliberate twisting. Or Seasick(Dizzy + Sea)
[] Yun Cai
Intended meaning: Colorful/Prismatic Clouds
This is both a literal description(in that we're generating mist everywhere and causing rainbow effects wherever the light hits it), and also an auspicious omen, in that prismatic clouds are one of the general signs of blessings and good fortune, as well as Immortals presence
Unintended meanings: Relatively few here,most requiring a deliberate stretch.
-Yun(Cloud) can also be Luck(neither good nor bad, just random) on a different tone, Transport, or Dizzy on yet another.
-Cai(Color) can also be Wealth, Talent, Lumber on a different tone
-Which means it could be
--Treasures/Talents of the Clouds(Cloud + Wealth/Talent)
--Auspicious Colors(Luck + Color, the purely random element having been mitigated due to the colors invoking particular kinds of luck)
--Lucky Talents(Talent mitigating the random element).
--It could also be Delivering Wood(Transport + Lumber)
--Dizzy + X implies being drunk on any of the Cai meanings, or more literally Dizzy/Confused Cai, which I don't think anyone has the balls to imply in setting, considering it takes actual effort to twist it.
[] Shaungyao
Intended meaning: Frost Rumor/Rime Rhyme
Not sure what it intends to mean, since I can't find any obvious associations beyond the most literal.
Unintended meanings, most of which are phonetically distant but again, deliberate twisting to mock is easily arrived at
-Shaung can mean Frost, Double, Pleasure
-Yao can mean Rhyme, One, Freak/Demon/Youkai, Bite, Drug
Somewhat too many viable nasty meanings for my taste, since Frost Demon Village is a bit too on the nose
[] Shenglu
Intended meaing: I'd just copy from the proposal(As an english name, to match style, something like Sacred Dew, Saintly Dew, Dewtown, Verdant Dew (the green was relevant after all!)... is probably best.)
Generally positive associations with a lot of positive readings from homophones, already fully elaborated in its own post
Threads Of Destiny(Eastern Fantasy, Sequel to Forge of Destiny) Original - Users' Choice!
Unintended meanings:
-Sheng has a lot of positive associations, about the worst I can get out of it is Raw(as in raw meat). Life, Rise, Victory, Holy.
-Lu likewise is a highly positive word, though I'm sure everyone is going to just focus on Prosperity/Success(Lu) and Deer(Lu), while Road and Dew also represent.
All round a sound name.
[] Yuanyin
Intended meaning: 源银 Yuanyin (Source of silver)
Its more Original Silver(Source of Silver is the other way round). I'm somewhat uncertain about defining your town around a mineral resource than could deplete however.
Unintended meanings
-Meaning - Origin(Yuan) Purpose(Yin), any chinese speaker would assume this first, no stretch needed.
-Yuan can mean Origin, Round, Grudge, Complaint
-Yin can mean Silver, Win, Vice(specifically prostitution), Sound, Shadow, Yin, Impression.
Some bundle of problematic associations here. Others could probably just ignore the prostitution implication, but we can't.
[] Xinyuan
Intended meaning: 新源 Xinyuan (New origins)
Fairly self explanatory as a descriptive, but it may have difficulty actually being representative of the name unless you're making a habit of taking in criminals and exiles for a fresh start.
Unintended meanings:
-Xin can mean Heart, New, Star, Hope
-Yuan can mean Origin, Round, Grudge, Complaint, Wish
All told harmless enough, beyond being more descriptive than aspirational.
[] Cloud Sea Town
This is just the Yunhai vote in english.
[] Snowmist Town
Intended meaning(?): Xue(Snow) Wu(Mist).
Well, it IS descriptive. Not good on aspirational though.
Unintended meanings(note this is a second order extrapolation):
-Xue can mean Snow, Blood or Learning
-Wu can mean Mist, Black/Dark, Nothing(lacking something), Dance, Martial, Object.
Quite a lot of nasty meanings in the chinese version, its one of those names you'd see the detective novelist put their whiteout locked room murder scenarios at.
[] Rimehearth
Intended meaning(?): Shaung(Rime) Wo(Hearth/Stove).
Relatively weak guess here, I'd need to research to find which specific words are best fit, but its only got the one vote so *effort*.
Unintended meanings(note this is a second order extrapolation):
-Shaung can mean Frost, Double, Pleasure
-Wo can mean a Wok, nest, yourself(the word for yourself that is), stove, grasp/hug
Mmm, it COULD mean hugs...
[] Mist Blossom
Intended meaning(?): Wu(Mist/Fog) Hua(Flower).
Mostly just a descriptive + reference here?
Unintended meanings(note this is a second order extrapolation):
-Wu can mean Mist, Black/Dark, Nothing(lacking something), Dance, Martial, Object.
-Hua can mean Flower, Culture, Expense, Speech
Nothing immediately standing out, though using Mist immediately packed a bundle of negative side meanings in by default.
[] Shenwu
Intended meaning(?): Deep Fog/Mist
Another descriptive name
Unintended meanings
-Shen can mean Deep, Save(as in save money), a specific category of Aunt, and Kidney
-Wu can mean Mist, Black/Dark, Nothing(lacking something), Dance, Martial, Object.
Nothing immediately standing out, though using Mist immediately packed a bundle of negative side meanings in by default.
[] Frost's Edge
Failing to map correctly without specific research effort
[] Dire Chuanxi
Intended meaning: Geothermal Respite
Too many words(its at four when usually you'd have two) to make a snappy name, I think, and it has accidentally arrived at a pinyin that is ALSO a valid english word. And I'm pretty sure Chuanxi is Respite as a time, not a place.
Not doing the unintendeds for four words.
[] Sacred Dew
[] Sacred Dewtown
[] Verdant Dewtown
These are just Shenglu translations.
[] Winter's Hearth
Intended meaning(?): Dong(Winter) Wo(Hearth/Stove)
The meaning gets twisty since Winter isn't a person capable of having stoves, so its just a specialty Winter Hearth/Stove. Its a kotatsu!
Unintended meanings
-Dong can mean Winter, Understanding, Motion.
-Wo can mean a Wok, nest, yourself(the word for yourself that is), stove, grasp/hug
Nothing bad here, some funnies.
[] Winter's Rest
Failing to map correctly without specific research effort, since I think the closest term just means Hibernation
[] Dongwu
Intended meaning: 冬霧 Winter Fog
Its a descriptive, so it doesn't meet GG's request.
Unintended meanings
-Any chinese speaker will read this as Animal(Dong[Moving] Wu[Object])
-Dong can mean Winter, Understanding, Motion.
-Wu can mean Mist, Black/Dark, Nothing(lacking something), Dance, Martial, Object.
[X] Yun Cai
[X] Shenglu
So I'd just go for the two names without immediately standing out problematic implications, which are aspirational or auspicious rather than just descriptive.