I notice that when custom car engines are sold they nearly always have a big name type name like "Ford" or "Chevy". Is this because the block and crankshaft comes from those companies and the custom engine company makes everything else, or for some other reason? Why can't custom engine companies make the whole engine?
There is no reason in principle why a custom engine builder couldn't cast a block themselves. Everything done by the level of automation in this process could by done by hand, given enough highly skilled craftsmen.
Whether there are customers who would want to pay for a hand-made block which costs as much as the rest of the car is another question.
The other issue is that if you want to replace the engine in a production car, rather obviously you want something which has the same mechanical interfaces to everything else in the car. So unless you want to cast it from a different material for some reason, you might as well start from a standard block that already fits.
First, because designing a car engine takes an incredible amount of engineering. It's not something that someone just sits down and does in an afternoon.
Second, because a "custom built" XYZ engine (302 Ford, 427 Chevy, whatever) is going to be much closer to a bolt-in replacement to a same-type engine. A typical 65-75 small block Chevy engine won't even physically fit into the engine compartment of a typical 65-75 Ford, and visa-versa -- the companies arranged their cars differently, and the oil sumps are at opposite ends of the engines. So even if you didn't get murdered by Ford fans for doing it, it would be a job and a half to put a small-block Chevy into a Boss 302 Mustang -- and ditto for a 302 Ford into a Camaro.
Third, there's this thing called "brand loyalty". Even though I'm not possessed of much of it, if I have some nice Chevy, I'm probably going to want to put a Chevy engine in it. Ditto Ford with Ford or Dodge with Dodge. You might find me putting a small-block Chevy into a Henry J, though.
Is this because the block and crankshaft comes from those companies and the custom engine company makes everything else, or for some other reason?
Usually, yes. Custom engines come in various stages of tuning. Stage 1 is pretty close to a stock engine, with just a few components replaced. Those replaced components have to fit the original engine. The more power you want to generate, the more components you need to replace. They still all need to fit the original engine.
For extreme applications (top-fuel drag racing), you can get engines where every component including the block has been custom-made and all that's left of the original engine is the main dimensions (distance between piston centerlines, distance between crankshaft main journals etc). These main dimensions remain because that means many of the parts are compatible across their entire catalog: a billet crankshaft that fits stage 3-7 is cheaper to make than a crankshaft that's unique to your 'everything is custom' stage 7 offering.
Why can't custom engine companies make the whole engine?
They can, it's just very expensive, and usually not necessary.
Big car companies produce engines by the thousand, and they have an assembly line set up to do this quickly and efficiently. Custom engine companies don't have the production volume to be able to afford this, so they have to spend more manual labor and machine time to build an engine. Things like the engine block are complicated to manufacture (requires big infrastructure for iron/aluminium casting, or a very expensive 5-axis CNC machine to mill the whole block).
So they only build the parts they really need to. A stage 1 tuning package doesn't require a new block, because the standard block has enough margin built in to handle the extra power.