Merchant Mariner, tall-shipper, and all round boat guy here:
It's not a dry dock. "Dry" implies the removal of the ship from it's operating environment. If it is designed to operate in a vacuum, with no gravity, a 'dry dock' would mean removing the ship into a pressure-controlled chamber with artificial gravity and atmosphere. Launching a ship into a body of water is similar to launching a rocket from a planet, into space. Where it belongs.
One of my BIGGEST pet peeves in space games is the use of the term 'dry dock.' It is simply, a 'dock.' That's all. No 'dry.' Also, it wouldn't be a dry dock in space. It's already dry. Nothing was wet to begin with. It's an Air-dock, or Pressure-Dock. Not a 'dry' dock. Instead of "Yeah, I'm getting hauled out", the phrase in space-faring would be more aptly, "Yeah, I'm getting hauled in," or "My ship's in on the dock," etc. Or maybe "My ship's chambered at the moment, another 3 weeks til launch again." That's elegant, even. Chambered. Heh.
Also - shipyard would work. Sometimes shipyards HAVE dry docks. But not all do.
Finally - Ships have many things that happen to them in yards and docks, and dry docks, but the only reason you would EVER go through the trouble of hauling a ship out on the dry, is for hull testing, or for work that requires holes, or patching, that cannot be accomplished with the ship in it's operating environment. Minor welds above waterline, painting, even sometimes engine repair and removal/replacement, can allll be done while the ship's in the water. Dry dock is always a last resort. It's expensive, and time consuming and all around will add 3 weeks to whatever estimated time of repair you had in mind.
Another pet peeve - I always see 'welding' happening in these 'space dry docks' everyone likes to mislabel. You know what I don't see? I don't often see connections for power, life-support, or water. In a dry dock situation, you shut your generators down. You shut ship-board power supplies down. Shut your water-makers or reclamation down. If you HAVE to get hauled out for any reason or even go to a yard and pay for slip space while you're there, you CAPITALIZE on that time, and do any and every project you think you can, even if it might not directly need it, because you're paying to be there, and don't want to come back soon.
Most likely, you're in yard because one of those needs maintenance, which requires you be hooked to station support while it's off line for the ship to continue functioning. Which means cutting a hole in the side of the boat or the deck, to remove the unit and repair/replace it. In the mean time, you run systems support lines to the ship like an IV at a hospital, so that those living aboard during the yard period have running water, heat, power, food. You have multiple connections to the ship where entry ramps for crew, ports for stowage and dunnage, and things like trash and waste can be transferred back to the yard for disposal, and access to normally-sealed ports where maintenance and equipment can attend to business.
If any one of you folks ever designs a game that has space ports - please, please consult a real sailor about what goes on in yards and dry docks. We'd be HAPPY to help you create a plausible, immersive ship yard in your game.
And for the love of all that is holy - if you're making a ship for Elite Dangerous - consult someone who knows something about physics. You will never have a ship that has no space for plumbing, coolant lines, or any other machinery space that actually runs the ship, and you would never, EVER put a guest quarters right up against a bulkhead that has a massive engine behind it, which is literally just a magic nozzle, because where is the actual engine attached to it going to go? ::Sigh::
To reply to the original idea: Call the object the Orbital Assembly Module, Space Assembly Module, or Colonial Assembly Module or something similar. I feel like 'Module' would work well with some combination of acronymmable adjectives.