The modern place names Spain and Hispaniola are both derived from Hispania.

What is modern day Hispania?

Hispania, in Roman times, region comprising the Iberian Peninsula, now occupied by Portugal and Spain.

What is Iberia called today?

The word Iberia is a noun adapted from the Latin word "Hiberia" originating in the Ancient Greek word Ἰβηρία (Ibēríā), used by Greek geographers under the rule of the Roman Empire to refer to what is known today in English as the Iberian Peninsula.