Identify this seafood from the Black Sea known in Romanian as "rapane"?

This is definitely a rapa whelk. These are indigenous to the seas in the far East, but got somehow imported into the Black Sea and overtook the ecosystem.

First, people around the Black sea didn't have much use for them. The waves washed the shells of dead whelks ashore and these got crafted into souvenirs for tourists. Then, people started fishing them and selling them to the Japanese, who ate them. At last, around the summer season of 2000 or 2001, restaurants along the western shores of the Black sea started offering them as food to their guests. Still, I think that much more of the catch is exported than consumed locally (but have no hard numbers for this).

Since the only people who eat them seem to be Japanese and recently also Bulgarians and Romanians, I highly doubt that they have a kitchen-specific name in English, or that you can buy them at all outside of the above locations.

Biologically, they're not related to oysters. My speculation is that innovative restaurant managers who wanted to serve them had to come up with a name which sounded like something posh (sea oyster) as opposed to one which is both common and associated with kitschy ashtrays (rapane).

They look like a species of whelk, which is a catch-all term for sea-snails. See the Wikipedia article here.

The following method works better than a dictionary most of the time when you have to identify plants or animals.

1. Open the Wikipedia home page, and search for "rapane" in Romanian.
2. Result #1 is rapan? (I don't speak Romanian, but I guess it's the singular), and a cursory look at the pictures confirms that it's the same shell.
3. On the left sidebar, look for the section "in other languages", and click on "English"
4. You are redirected to the English page for Veined Rapa Whelk.

That's a bingo! Even a non-expert, non-Romanian like me could identify this species with no effort.

It's a conch, the common name for an edible marine snail. Not an oyster for sure. :)

In Ukraine these are sold preserved in jars with oil and spices, one of their kinds is called "Antalya". If they are popular in Turkey too, or this is just a marketing name - I don't know.