The Endless do have specific human forms. Gaiman either came up with them all or borrowed/stole them from others.
* Dream has been an alien-looking white guy with straight black hair ever since the series was first pitched, with sketches by Gaiman, McKean, and Baulch.
His second aspect is a grown-up form of Lyta and Hector Hall's kid, the son of two pre-existing characters he incorporated into Sandman.
* Death was originally supposed to look like
Nico, but the artist modeled her on
Cinamon Hadley and Gaiman approved that.
* Destiny was a
pre-existing character.
* Desire is just that Patrick Nagel
woman, the one you used to see in nail salons and tanning parlors.
* Despair is Desire's twin and should be equally white.
* Delirium first appeared as a teenage scene girl so I wouldn't be surprised if she was modeled after someone Gaiman or an artist wanted to fuck. She's also a redhead, so we know what they're going to do to her. Bonus points if they just rehire Crazy Eyes from Orange Is The New Black.
* Destruction was evidently modeled after Brian Blessed before Jill Thompson gave him a less imposing physique.
It's true that the Endless look different to different people--Dream is an African when speaking to Nada and a cat when speaking to other cats, Delirium is Asian when working the San Francisco opium dens--but 99% of the time they have their normal appearance, even when no humans are around. Because that's what Gaiman wanted them to look like. The artists worked in their own styles, but they were always working from the same designs.