OK, just a passing thought. Would it be possible to prevent rise of Spanish/Iberian/whatever identity?
No. "Spanish" identity came from the visigoth kingsom of Hispania (the one conquered by the moors). All the christian sucessor nations (Asturias, Leon, Galicia, Navarre, Portugal, Castille, Aragon) considered themselves (and, depending of the particualr relations at the moment, their sibling nations) as the rightful heirs to Hispania. In fact, Portugal was very offended when the Catholic Monarchs named the union of Castille and Aragon "Spain" -a different Portuguese identity would not truly form until later, when Portugal and Spain had each conquered their own empires.
Still, a more succesful islamizacion IS possible, but, as Bastian said, you'd simply get a Spain named "Al-Andalus". There would be two Islamic Empires in the mediterranean, the Ottomans on the East and the Andalusi on the west.
An interesting butterfly -Al-Andalus, until it was weakened by the christians and then conquered (twice) by muslin "puritans" -the Almoravids and the Almohads, was a very enlightened society, which translated most Greek works. Since the POD is around the eight century (conquest 711, Battle of Covadonga 722, battle of Poitiers 732), the Renaissance could come from the muslims TTL (note than islamic religion does not forbid human images; they forbid human religious icons, like the Catholic saints. There were scultures of sultans in Al-Andalus, and even illuminated Kurams with Mohhamed and his followers in Persia)