>1. 聖剣・蕩塵
Holy Sword・Scattering Dust

> 2. 耆・天狼
Ancient ・Sky Wolf (Sirius)

>3. 墨淵玄離
Abyssal Phantasmagorical Disappearance
Literal translation would be "ink deep mystery leaving", which is nonsensical. Also, there's like a multi layer reference in this shit.
(1) 墨淵 and 玄離 are apparently the names of some other wuxia works. 玄離 in particular is a character from another Pili puppet show.
(2) Gen Urobuchi's name is 虚淵 玄, so he basically snuck (part of) his name into the sword.

>4.魔劍・墮日斬
Demonic Sword・Sky collapsing Cut

>5.喪月・死寒魄
Mourning Moon・Deathly Cold Spirit

>6.幽冥・萬世神伏
Netherworld・Unlimited realms of Lurking Deities
伏 can mean conceding defeat or ambush as well. So alternate interpretations could be
- Deities Ambushing from Unlimited Realms
- Taming of Deities of Unlimited Realms

>7.飲雪
Drinking/Consuming (the) Snow

>8.喪月之夜
Can mean either Night of the Mourning Moon or The Night where one Mourns the Moon

>9.孤煞瀾月
Lone Phantom of the Rippling Moon

>10.冥幽玄牙
Enigmatic Dark Fangs of Underworld Spectres

>11.百代昆吾
Hundred Generations of Kunwu
Welp, time for more references. Kun Wu is supposedly a famed blacksmith (whether he's a real historical figure, or just a legend, or mix of both, that's still up to debates). Kun Wu's weapons thus are supposed to be top tier stuff.

> 12.妖姬・七殺天凌
Demonic Princess・Seven Killings in the Heavens

> 13. 須彌天幻・劫荒劍
Illusory Skies of Meru・Plundering the Abandoned Sword
須彌 refers to Mt Meru. According to wikipedia, it is a sacred mountain with five peaks in Hindu, Jain and Buddhist cosmology and is considered to be the centre of all the physical, metaphysical and spiritual universes.
To add to that, in buddhism there's a phrase/concept of "納須彌於芥子", or "containing mountain Meru in a speck of dust". Considering the theme of the sword is space-time manipulation, it's oddly fitting.

>14.青燈孤照
Green or Young Light Shining in Solitude

>15.鳳刀蝶殺
Phoenix Blade Butterfly Slaying

>16.炎殺・雷岳
Killing Blaze ・Thunder Mountain

>17.斬・日月
Slay・Sun Moon

>18.炎邪黯刃
Blazing Evil Dusk Blade

>19.霹雷鳴劍
Sword of Thunderbolt's (here's your obligatory studio namedrop) Roar

>20.靂降風雲
Descend of Crashing Thunder, invoking the Unforseen
風雲 literally means Wind and Clouds, but the implication is supposed to be unpredictable changes or tidings.

>21.狂鳳玄牙
Enigmatic Fangs of the Wild/Arrogant Phoenix

>22.刀影破
Broken/Breaking of the Blade's Shadow

> 23.舞羽孤蝶
Dancing Feathers Lone Butterfly

>24.東風瀾月
Eastern Wind Rippling Moon

>25.離寒破辰
Leaving the cold, breaking dawn

>26.劍皇破佛
Sovereign/Royal Sword Denouncing the Buddha

>27.畫影空騰
Drawing Shadows (and) Taking Flight into the Void/ Nothingness

>28.鎮嶽尚方
Suppressing (the mountain) Peak, Sword of State
尚方is a reference to尚方寶劍, the sword that symbolizes the rule/power of the monarch.

>29.龍淵
Dragon in the Deep/Abyss

>30.荒夢赤霄
Forgotten Dream, Scarlet Mist

>31.六道殊月
Six Paths of the Peculiar Moon
The six paths is yet more references to Buddhism. Wiki Samsara for more details.

>32.流光劍
Chronos Sword; literally means 'flow of time sword', so I'll put it as Chronos Sword to make it more chu2

>33.古龍青雀
Ancient Dragon, Green Sparrow

>34.日月神息
Unending Pulses of the Gods

>35.九天玄冥
Nine Days of Xuan Ming
Xuan Ming historically refers to a type of northern god/deity of winter, implying the lack of sun

>36.六問虛空Prashna Upanishad
六問虚空
六問 6 Questions (A reference to the Prashna Upanishad)

>How did life begin
>What is a living being?
>What is the nature of man, and how is it so?
>What establishes man?
>What is meditation, and why meditate?
>What is immortal in man?

虚空 Empty Air / Void / Meaninglessness
虚 combines with 淵玄 from . 墨淵玄離 to form Gen's name

Figuratively, an existential crisis