The "costume" is actually a living creature that needs to bond to another living organism in a symbiotic relationship, which has given rise to the practice of calling the living costume a "symbiote". Once bonded, the host and symbiote behave as one entity.
As other answers have pointed out, the white areas of the 'mask' on the symbiote known as Venom are facsimiles of the one-way lenses used in the mask of the original red and blue Spider-man costume. As such, we can surmise that they behave the same way, allowing the wearer/host to see out but preventing anyone from seeing through from the outside.
I don't have any knowledge of whether or not the unbonded symbiote has a way of seeing. Since the symbiote itself feeds of the neurological chemicals of the host's brain, it's possible that the symbiote does not in fact see at all on its own, but only through the host's optical nerve impulses. We can thereby extrapolate that Venom's eyes are, in fact, the host's eyes.
That said, the appearance of the Venom symbiote's eyes is largely dependent on the host that the symbiote is bonded to, though subsequent iterations are variations of their appearance when it was bonded to its "first" host - Peter Parker. (I realize that certain storylines in the comics retconned some additional hosts before Peter in-universe, but since the first true appearance in the comics was when it was bonded to Peter, that is the original appearance from which all others are derived). Some of the most important variations are:
When bonded to Peter, the shape is a relatively uniformly curved "cat's eye" that, per above, is based on the same area of the red and blue costume.
When bonded to Eddie Brock, the first host to bond with the symbiote after Peter, thereafter known as Venom, the eyes take on a variant fluid, distorted, twisted version of the original "cat's eye" shape. It's worth noting that this was an evolving look, originally only taking on a more sinister, exaggerated proportion and shape:
But ultimately being distorted to an almost fluid-like shape in the first pic, as though the edges are constantly ebbing and flowing. This obviously is dependent on the artist's interpretation of the character.
Venom II/Mac Gargan
Later, the symbiote is auctioned off by Brock and purchased by a mob boss for his son to use. The symbiote rejects the mob boss' son and bonds instead with Mac Gargan, formerly known as the Spider-man villain Scorpion. As you can see, the white areas of the eyes actually form more of what you describe as the "Orca Whale" pattern with a distinctly visible eyeball, similar to the fan art you posted. It is again worth noting here that further down the line, the symbiote is administered a medicine of sorts by Norman Osborn in order for it to be more docile and take on the appearance of the original black costume worn by Spider-man, in order to appear as the real Spider-man in Osborn's "Dark Avengers" as "The Sinister Spider-man".
Agent Venom/Flash Thompson
When bonded later to Peter Parker's high school tormentor/war veteran Flash Thompson, the eyes take on a similar shape to the original but as only a white outline with a black inner area. Presumably the one-way visibility is retained, where the host can see out of the black area, but obviously no one can see through from the outside.