In scandinavian languages (including Finnish, which hints at the fact that they don't have a lot of rabbits there) it's very similar: "kanin", pronounced ka-neen. Apparently it traces via old French and German back to the Latin "cuniculus" which actually means rabbit.
Meanwhile, "hare" (or "Hase" in German) remains also in English.
Spain was named by the Phoenicians after the huge number of rabbits they saw there. But they had no word for rabbit, so they used their word for hyraxes.
Which are, by the way, the closest extant taxon to the elephants. Which themselves are named just for their thick skin.
Hyraxes, in turn, look rather like chunky ferrets. As you say, they aren't closely related, but i suppose if you're a mammal which lives in holes in the ground, there aren't many body shapes which work.
