I would like to discuss some points that are being commented on this thread.
About of the titular (or marketing) airline for these new services, the best bid would be Vueling. Actually they also fly under the Spanish (and European) flag, next to the aircraft registration code, but it has a much more Catalan and low-cost feeling than Iberia. Anyways, one could perfectly say that Iberia's colors match perfectly those on the Catalan flag, and that Iberia is a word that encompasses all countries in the Iberian Peninsula, not only Spain. But it is true that Iberia has not used Barcelona as a hub in a long time, even if it is still indicated as such in the in-flight magazine.
Other option discussed here was resurrecting some former IAG brand. Air Liberté or Go would not be really appealing, I guess. Former Spanish IAG brands were Aviaco and Viva. Viva was more of a vacational Lufthansa+Iberia airline, so my bet would be Aviaco, the second Spanish airline until the 1990s.
As for the operating airline, if they prefer an in-house operator, that should be Aer Lingus, with Iberia as a second option. I have seen someone suggesting Wamos as an outsourcing option, but at this moment they only have 1 332, and 5 744s of which 4 are in Conviasa and Saudia. Evelop has 2 333s and Plus Ultra has 2 343s (soon 3), to say other Spanish options, aside from Air Europa, that would not want or be able to cooperate.
Last summer, for relieving their capacity crisis, Vueling leased, at some point or another, planes from Plus Ultra (340), Wamos (747), Privilege (757/767), Avion Express (320), Evelop (320/330), Titan (320/757), Air Nostrum (CRJ1000), Euroatlantic (767/777), AirExplore (737) and White (320), so maybe the 330s could be leased from some of these companies.
Finally, someone said about expanding Meridiana in Italy and to Spain, now that they are "cousin" airlines to IAG. Last time Meridiana expanded to Spain they ended up closing the Spanish operations, but maybe a second try could be better than the first. Anyways, this option would be more in control of Qatar than of IAG, so I guess this is not going to be the plan.