Shouldn't this be in the Before 1900 section?
Still, I do feel like contributing. Firstly, I think it would be unlikely that any republic would be named Iberia unless it controlled the whole of Iberia. Spain would be the likely name of a union between Castile and Portugal, just as it was between Castile and Aragon.
Secondly, in my opinion, keeping Aragon independent would be very hard. All Iberian nations used to consider themselves Iberian, the Portuguese were greatly offended when the union of Castile and Aragon decided to call themselves Spain, since they believed themselves to be 'Spanish'. They only began to move away from that when they had their own colonial successes.
For Aragon to remain independent they would need some sort of achievement that sets them apart from the Spanish nation, a sort of 'look at me, I did this all by myself' happening. Without an Atlantic coast, and thus ease of access to the America's, gaining this national pride would be much more difficult than it was for the Portuguese.