The european rabbit (and the domesticated rabbit, which descends from it) is native to the Iberian peninsula. There are ~20 extant species called rabbits all over the world (most though not all leporids outside of Lepus, the true hares).

well they are native almost everywhere but according to legend it was named i-spn-ya (Land of the Rabbits) by the Phoenician although some suggest that SPN could also have meant North instead of rabbits so land of the north.

If I recall, the word 'España' or 'Hispania' refers to an old word for 'hyrax', for which rabbit were mistaken for. Could be apocraphyl but it's a nice idea.

Within Europe, you mean? A quick Google suggest there were native rabbits also in the Americas, Asia, and Africa.