The five main, major companies each have their own design and specialty, and these are in the areas that determine the outward-facing appearance of the ship - structural elements, cockpits, and even the ship’s inside spaces.

The other ship companies are all more generic, and make things like weapons, fuel storage, and cargo hold ship inventory expansions - basically, stuff that has less of an impact on the overall style of your ship, more the actual functionality. The ‘generic’ ship modules can be found almost anywhere, including most places that you find ship techs, which is the landing bays at all major and even some minor settlements. There will be a list of these at the end of the guide. If you find any that are not on the list, please comment below and I'll add them.

Keep in mind that the vendor's stock is partially random, so item availability is not guaranteed. If you're not seeing what you're looking for, try waiting for 48h to reset the vendor inventory. It's also worth noting you unlock more ship modules as you level up. All ship modules are available at level 60 (These don't show up until you've met the level requirement)

Feel free to ask any questions in the comment section, either me or perhaps other members of the community could help you out.

If you're interested in the interior of the ship modules I recommend this post.

If you're having trouble figuring out what to buy and use on your ship, here's a guide with all the stats and requirements for non-cosmetic ship modules. https://test-steamproxy.haloskins.io/sharedfiles/filedetails/?id=3034554203

Deimos, Mars, Sol
Deimos has a staryard in the Sol star system orbiting Deimos, a moon of Mars. You'll need to travel to Deimos and dock the staryard.
When you enter the staryard you'll want to go straight forward, passing the reception, then at the end of the hall you want to go down the stairs to the left. There you'll find Nikau Henderson who will sell you the ship and ship modules.

• There’s exclusive cockpits, landing gears, structures, and some large-sized habs.
  
• Known for sturdy ships and solid ballistic weapons.
  
• Stroud-Eklund and Deimos have the best workshop as they have not only the crafting tables but also a research terminal, meaning that with a single workshop you have every crafting station except pharmaceutical.

Source

Hopetown, Polvo, Valo
Hopetech has an office in Hopetown which is located in the Valo star system, on the planet Polvo. You won't see Valo on the star map by default. You'll need to hover the Narion system to see Valo in the drop down menu.

Once you land in Hopetown you'll see the Hopetech office right in front of you. Just walk through the front door.
On the inside you want to walk through into the main room and you'll see the sales person on your right behind a counter. Her name is Inaya Rehman.

• Known for great general ship modules like structural, gear, and dockers.
  
• Exclusive cockpits, dockers, landing gears, structure pieces, and a large number of habs.
  
• Has few very unique cockpit pieces that attach to the ship from the top - meaning the cockpit can sit underneath the body of the ship as opposed to at the front or the top.
  
• Unique ‘fuselage’ shaped hab elements.

Source

New Homestead, Titan, Saturn, Sol
You'll find Nova Galactic in the Sol system, in the New Homestead which is on Titan, a moon of Saturn.
The vendor is the Ship Services Technician on the landing pad, directly on your left as soon as you land.

• Famous for its Habs, Landing Gears, and Structural parts.
  
• Enormous 3x2 habs, and a brilliant 3x2 cockpit, plus one of the most powerful landing gears in Starfield.

Source

Dalvik, Deepala, Narion
The Stroud-Eklund Staryard orbits Dalvik, a moon of Deepala in the Narion system.
Once you dock the staryard and enter you'll come out of the red door in the screenshot above on the left. You want to keep going forward into the office and on your left you'll find Havershaw behind a desk. He'll sell you the ships and ship modules.
Alternatively you can visit the Showroom in Neon Core on Volii Alpha in the Volii system. You can use the kiosk behind the woman to both buy ships and ship modules. Both Havershaw and the kiosks seem to have the same inventory.

• Unique landing bay, cockpits, dockers, landing gears, and more.
  
• Luxury interiors and sleek design.
  
• Stroud-Eklund and Deimos have the best workshop as they have not only the crafting tables but also a research terminal, meaning that with a single workshop you have every crafting station except pharmaceutical.

Source

Neon, Volii Alpha, Volii
You'll want to land in Neon, more specifically Neon Core (You won't be able to fast travel here unless you've already visited Neon Core before). The city is located on Volii Alpha in the Volii System.
Once in Neon Core, depending on whether you fast traveled here or entered through the elevator, you're looking for a red Ryujin Tower. If you fast traveled it'll be on your right. If you entered through the elevator, it'll be on your left. It's all the way at the end, you can't miss it. Just walk straight forward to it once you see it. You'll encounter an elevator. You want to enter it and click Taiyo Astroneering in the menu.
When you exit the elevator you want to go to the right, then down the stairs to the right again. There you'll see Veronica Young, which is the sales person.

• Unique Bays, Cockpits, Dockers, and Habs, plus structural parts with Taiyo’s unique sense of style.
  
• Know for state-of-the-art cockpits, habs, and gear.

Source

There are many other ‘generic’ manufacturers - these have a variety of names, but these companies aren’t ones you can visit specific offices for. Instead, you’ll find their products scattered across all of the various Staryards and Landing Pad Ship Services technicians you can visit across Starfield’s Galaxy.

These generic ship module manufacturers are and specialize in the following:

• Amun Dunn: Power Reactors
  
• Ballistic Solutions: Ballistic Weapons, Fuel Storage
  
• Deep Core: Grav Drives, Cargo Storage
  
• Dogstar: Cargo Storage, Reactors, Shields
  
• Horizon Defense: Weapons
  
• Light Scythe: Energy Type Weapons
  
• Nautilus: Fuel Storage, Shields
  
• Panoptes: Engines & Cargo Storage
  
• Protectorate Systems: Cargo Storage
  
• Reladyne: Grav Drives, Engines
  
• Sextant Shield Systems: Shielded Cargo Bays, for hiding Contraband
  
• Shinigami: Energy Type Weapons
  
• Slayton Aerospace: Grav Drives, Engines
  
• Xiang: Power Reactors

Not all landing pad ship technicians in Starfield are equal - even when they’re not attached to a specific company.

The ship technician on Porrima III at the Red Mile sells shielded Cargo Bays, for instance. So too does the ship tech aboard The Key if you join the Crimson Fleet.

Plus, once you unlock a landing pad on your outpost, you'll get your own ship tech who tends to have particularly broad stock.

and what they sell.

New Atlantis, Jemison, Alpha Centauri

• Structural – Horizon Defense, Deimos, Nova Galactic
  
• Shields – Dogstar, Sextant Shield Systems
  
• Reactors – Amun Dunn, Dogstar
  
• Habs – Demios, Nova Galactic
  
• Grav drives – Deep Core, Reladyne, Nova Galactic
  
• Gear – Deimos, Nova Galactic
  
• Fuel tanks – Ballistic Solutions Inc., Dogstar, Nautilus
  
• Engines – Amun Dunn, Panoptes, Redalyne
  
• Dockers – Deimos, Nova Galactic
  
• Cockpits – Deimos, Nova Galactic
  
• Cargo – Sextant Shield Systems, Protectorate Systems, Dogstar
  
• Bays – Deimos, Nova Galactic
  
• Weapons – Horizon Defense, Light Scythe, Ballistic Solutions Inc.

Akila City, Akila, Cheyenne

• Structural – Nova Galactic, Taiyo Astroneering, Stround Eklund, HopeTech
  
• Shields – Dogstar, Sextant Shield Systems, Nautilus
  
• Reactors– Amun Dunn, Dogstar, Xiang
  
• Habs – HopeTech, Stround Eklund, Taiyo Astroneering
  
• Grav drives – Deep Core, Reladyne, Slayton Aerospace
  
• Gear – HopeTech, Stround Eklund, Taiyo Astroneering
  
• Fuel tanks – Ballistic Solutions Inc., Dogstar, Nautilus
  
• Engines – Amun Dunn, Redalyne
  
• Dockers – HopeTech, Stround Eklund
  
• Cockpits – HopeTech, Stround Eklund, Taiyo Astroneering
  
• Cargo – Panoptes, Protectorate Systems, Dogstar
  
• Bays – HopeTech, Stround Eklund, Taiyo Astroneering
  
• Weapons – Horizon Defense, Light Scythe, Ballistic Solutions Inc., Shinigami

Neon Shipyard, Volii Alpha, Volii

• Structural – Nova Galactic, Taiyo Astroneering, Stround Eklund, HopeTech
  
• Shields – Dogstar, Sextant Shield Systems, Nautilus
  
• Reactors – Amun Dunn, Xiang
  
• Habs – Stround Eklund, Taiyo Astroneering
  
• Grav drives – Deep Core, Reladyne, Slayton Aerospace
  
• Gear – Stround Eklund, Taiyo Astroneering
  
• Fuel tanks – Ballistic Solutions Inc., Dogstar, Nautilus
  
• Engines – Panoptes, Redalyne
  
• Dockers – Taiyo Astroneering, Stround Eklund
  
• Cockpits – Stround Eklund, Taiyo Astroneering
  
• Cargo – Panoptes, Protectorate Systems, Dogstar
  
• Bays – Stround Eklund, Taiyo Astroneering
  
• Weapons – Horizon Defense, Light Scythe, Ballistic Solutions Inc., Shinigami

Unless stated otherwise these can be found on/near the landing pad.

• Hopetown, Polvo, Valo
  
• New Atlantis, Jemison, Alpha Centauri
  
• Gagarin, Alpha Centauri
  
• Neon, Volii Alpha, Volii
  
• The Eleos Retreat, Ixyll II, Ixyll
  
• Paradiso, Porrima II, Porrima
  
• New Homestead, Titan, Saturn, Sol
  
• The Den, Chthonia, Wolf
  
  • Right in front of you when you dock and enter The Den.
• Cydonia, Mars, Sol
  
  • Outside, to the left of the entrace to Cydonia.
• Akila City, Akila, Cheyenne
  
  • Can be found in a small shed right outside the landing pad. Just follow the path.
• Red Mile, Porrima III, Porrima - Sells shielded cargo and Scan Jammers.
  
  • Sitting inside an office right in front of you when you enter the main Red Mile door. His name is Lon Anderssen.
• The Key, Suvorov, The Kryx - Sells shielded cargo and Scam Jammers.You can't visit this until you do the Crimson Fleet questline.
  
  • When you enter The Key - Cargo Bay and walk up the stairs, she's on your left. Her name is Jasmine Durand.
    
  • If you side with the Crimson Fleet, you can buy the Comspike and Conduction Grid here after the questline.