Svalbard is an archipelago kinda north of Norway – really north of the North Sea, if you wanna get technical. Two of the main islands are named East and West Spitzbergen, and the whole place used to be named after them.
Novaya Zemlya and Severnaya Zemlya are distinct critters. Both are island groups (named when they thought they were single islands) north of Russia. (The names mean New Island and North Island, respectively.) Nearby are the Novosibirskoye Islands. And there are several seas, generally frozen, that they separate one from the other, along the Siberian coast of the Arctic Ocean.
But how come nobody’s mentioned Ellesmere Island? Or Kerguelen? Or South Georgia (the island, not where Valdosta and Waycross are)?