space ships need to maximize heat dissipation, meaning a compact shape is bad.

In general spaceship forms follow function. A carrier might, for instance, have the entire battle groups of fighters docked to the outer hull instead of berthed in a bay, allowing them all to launch at once if needed. that might look like a four-shafted pitchfork, what with the drive sections commonized to the rear of the vessel. A tender craft capable of servicing four external vessels at a time might be configured in the form of a "plus" (or an 'X") as seen from overhead, allowing the vessel ample surface area for docking for each, with the engine nacelles running along the top and bottom

Is there artificial gravity? If so, shape may follow some arcane requirements based on that. If not, shapes could be hoops or cylinders which spin, to mimic gravity.

Do ships enter planetary atmosphere? Aerodynamics may apply if you're going to spend time not in space.

Look at the Apollo Lunar Module for what a realistic spaceship is going to look like: a central pressure vessel with bits stuck on wherever they're needed.

Nothing. You put the drive down the center of gravity of whatever shape you fancy, to avoid a high moment of inertia when you light the torch, but otherwise there is no preferred... wait. You want a sphere, because down is the direction opposite your drive, when it's on, but in free fall any direction you pick is down, so a sphere, with a drive down the middle, with weapons and sensors all over it.

The answer to this question is really defined by the limitations of the technology of your future, especially since you mention galactic, which implies faster than light travel.

Critically you haven't specified exactly what type of 'drive' your star ships are equipped with. If space travel in your universe involves sub light travel i.e. speeds less than but possibly approaching the speed of light then your ships (barring some 'unobtainium' tech levels) need a 'needle' like profile to reduce their exposure to radiation, molecular & particle impacts along the line of travel. If however the mode of transport is some kind of Star Trek like 'warp' field? Then the ship profile is limited only by the shape of the field itself. If its some kind of worm hole? Take your pick!

Are the ships pressurized? Other pressurized vessels (e.g. propane tanks) are often rounded to avoid weak points at the corners that would otherwise invite leaks and depressurization.

@rackandboneman Being stranded in interstellar/intergalactic space without power.

@Escapeddentalpatient it seems, in many science fiction stories any other condition would be considered newsworthy..... but seriously, if you were talking living quarters not engineering decks, you would basically have (body heat from organic occupants, waste heat from robots, waste heat from edge/endpoint electronics, heating by impinging inside and outside light (and other radiation), waste heat from activities like food prep, conducted heat via structure, hot objects) vs (heat loss) vs (the tab life support systems have to take)?

I'm tempted to vote to close as a duplicate of Optimum shape for a Space Dreadnought, itself closed as a duplicate of What shape of a ship would be most effective in real life space combat?. You've provided no limitations, conditions, or expectations for judging a best answer. Can you explain why those other two questions don't adequately answer yours?

"spaceships could be any shape due to a lack of drag." Inertial "drag" probably starts to matter a great deal when the ship is a kilometer long. The front might split off when you make a turn.

@rackandboneman not any ship with power and people inside. humans and machinery generate heat constantly. maybe if the ship was a simple cargo hauler with minimal crew, powered systems, and living space, then the thermal flux of the entire ship might be in the negative. But military ships would absolutely have a LOT of heat to get rid of, especially in combat.

@LOngfist On Earth, ships float partially submerged in water, while airplanes fly in the atmosphere which offers much less resistance, so even planes with tiny engines can travel much faster than even giant ships with giant engines. In space, all vehicles operate in a vacuum, so so mall military spacecraft analogous to airplanes have not advantages in space. There won't be any carriers in space.

Making it invisible or putting a giant blanket over it would stop a large spaceship from looking like a flying brick.

@M. A. Golding - you couldn't be more incorrect. As long as we require fuel to operate anywhere, and as long as F=MA there will be carriers. Specialization pretty much makes that happen. A single weapon-carrying platform can carry all the weapons it wants, but the surface area required for them to be deployed will start to interfere with how many can be deployed against a single target at a time, limiting that "massive advantage of 1000 weapons" to only a few hundred along a surface. A few nimble fightercraft eliminates that advantage and gives higher firepower. It's just history.

“boxes would be the easiest to manufacture” [citation needed] — you take this as given, but it depends on many variables. For centuries, glass was most easily manufactured as bottles or flasks; flat plate-glass was much harder. And boxes may have terrible structural stability — a pure box might be easy, but a box that doesn’t collapse under its own weight not so much. There are all sorts of reasons why boxes might not be the easiest form to manufacture at all.

You could take the Iain M Banks approach. Spaceships are absolutely huge, supporting populations of millions. Their shape is two-fold. The interior shape, which is where you add bits wherever you need them, & the exterior shape, which is a massive generally oval field, preserving all inside its envelope.

@LongFist Not to mention, distance and mission duration is largely limited by the human pilot. Carriers let your pilots eat, sleep, exercise, etc. during travel and only spend minimal time cooped up in a small craft with limited provisions.