Please note that this article contains spoilers, so don't read it if you haven't played the game and would like to at some point in the future.
I am also still busy updating and fixing the terrible formatting when I find a moment, please bear with me This is a long list...
Epistrophy - Kenny Clarke & His 52nd Street Boys
The Space in Between - How To Destroy Angels
I found two songs with the same name, but I think the How To Destroy Angels piece has Judy vibes to it, and it is a damn good tune. Listen here
Queen of the Highway - The Doors
The Highwayman - The Highwaymen
I'm not sure if this is correct, apparently the mission name is based on a poem, but a poem is not a song, so this is what I think it is. Listen here
Stadium Love - Metric
Talkin' 'Bout a Revolution - Tracy Chapman
I'll Fly Away - Hank Williams Sr or Johnny Cash
I put both here, since I like both, but according to the wiki page, it's the Hank Williams Sr one. Listen here - Hank Williams Sr Listen here - Johnny Cash
Send In The Clowns - Judy Collins
Kold Mirage - Lorn
Pyramid Song - Radiohead
Violence - Grimes
This is that mission where V needs to do something for Lizzy Wizzy, a celebrity in the game. Listen here
Coin Operated Boy - Dresden Dolls
The perfect song for the mission, I instantly recognised this when I saw it in the game. Listen here
I Fought The Law - The Clash
Sex On Wheels - My Life With The Thrill Kill Kult
I haven't heard this in ages, it's a classic! https://www.youtube.com/watch?v=PfsbLhptmS4
Chippin' In - Samurai (Refused)
A fictional band played by Refused, a real life band. https://www.youtube.com/watch?v=Igq3d6XA75Y
Fortunate Son - Creedence Clearwater Revival
It's pretty striking how fitting the songs are with the missions that were named after them. Whoever designed this a genius. https://www.youtube.com/watch?v=ZWijx_AgPiA
The Hunt - New Model Army
https://www.youtube.com/watch?v=j7K88HqFQ8M
Dream On - Aerosmith
https://www.youtube.com/watch?v=89dGC8de0CA
Space Oddity - David Bowie
https://www.youtube.com/watch?v=iYYRH4apXDo
Fool On The Hill - The Beatles
https://www.youtube.com/watch?v=wsRatIMUSu8
Sinnerman - Nina Simone
https://www.youtube.com/watch?v=QH3Fx41Jpl4
There Is a Light That Never Goes Out - The Smiths
https://www.youtube.com/watch?v=siO6dkqidc4
They Won't Go When I Go - Stevie Wonder
This is a path of the mission Sinnerman, after you make a certain decision in a previous part of the mission. This is a really heavy story and kind of made me feel rather sad, but in a good way. I wish I could convince him not to go through with it :( https://www.youtube.com/watch?v=cdTKdm8hZZY
Only Pain - Gojira
https://www.youtube.com/watch?v=fqLI8smRob0
Ride Captain Ride - Blues Image
https://www.youtube.com/watch?v=HqFFjoRnltg
One Way Or Another - Blondie
https://www.youtube.com/watch?v=_zBwRDEFMRY
From Her to Eternity - Nick Cave & The Bad Seeds
https://www.youtube.com/watch?v=A77f5pLnJlc
Moving Heat - Maenad Veyl
I'm not sure if this is correct, but it's the only song I could find online that fits this mission name. https://www.youtube.com/watch?v=pByQ97SyVmc
Unfinished Sympathy - Massive Attack
https://www.youtube.com/watch?v=ZWmrfgj0MZI
Last Call - Elliott Smith
I found a number of songs called Last Call, but this one seems the most appropriate and in line with the taste in music of the rest of the music the mission names are based on. I also think it's this one, because many of the other songs of the same title was released after the game was released in 2020. https://www.youtube.com/watch?v=jYj64QuOT1U
The Killing Moon - Echo & The Bunnymen
https://www.youtube.com/watch?v=LWz0JC7afNQ
Firestarter - The Prodigy
https://www.youtube.com/watch?v=wmin5WkOuPw
Voodoo Treasure - Majestic
https://www.youtube.com/watch?v=j-9yeOYwyxM
I've Seen That Face Before - Grace Jones
https://www.youtube.com/watch?v=nIN3IE3DHqc
Baby Let Me Take You - The Detroit Emeralds
https://www.youtube.com/watch?v=ihlZ7ISXUyU
The Show Must Go On - Queen
https://www.youtube.com/watch?v=t99KH0TR-J4
Dazed And Confused - Jake Holmes
Most people know this as a Led Zeppelin song, but it was originally written by Jake Holmes in 1967. https://www.youtube.com/watch?v=_-F8XGQ46c0
Shot By Both Sides - Magazine
https://www.youtube.com/watch?v=Qu3R-H5on1s
Money For Nothing - Dire Straits
https://www.youtube.com/watch?v=wTP2RUD_cL0
Addicted To Chaos - Megadeth
https://www.youtube.com/watch?v=B-YnLoozIAs
Birds With Broken Wings - Ben Caplan
https://www.youtube.com/watch?v=kfzy08FSdS4
You Know My Name - Chris Cornell
https://www.youtube.com/watch?v=0p7WZRL6I-8
Get It Together - Beastie Boys
The wiki page doesn't name a song, however I think this is the one. https://www.youtube.com/watch?v=0bkMtWL-5vM
New Person, Same Old Mistakes - Tame Impala
https://www.youtube.com/watch?v=_9bw_VtMUGA
The Damned - The Plasmatics
I'm not sure about this one... https://www.youtube.com/watch?v=DuGX188WmhY
Balls To The Wall - Accept
https://www.youtube.com/watch?v=B_3TlrZLpQ0
No Easy Way Out - Robert Tepper
https://www.youtube.com/watch?v=rOXaPE6gklI
Push It To The Limit - Paul Engemann
https://www.youtube.com/watch?v=3-3Yok5D3Aw
Lucretia My Reflection - The Sisters Of Mercy
https://www.youtube.com/watch?v=IuezNswtRfo
Spider And The Fly - The Rolling Stones
https://www.youtube.com/watch?v=TahNdsiCIYk
Hole In The Sky - Black Sabbath
https://www.youtube.com/watch?v=fg5p78QlqTM
Tomorrow Never Knows - The Beatles
https://www.youtube.com/watch?v=m4BuziKGMy4
Dog Eat Dog - AC/DC
https://www.youtube.com/watch?v=F8kjqWCCXvU