If the treaties of Tordesillas and Zaragoza happened in that alternate world, they would prevent such Oceania. Picture related:
I have no idea on where those lines would be set up. But they would almost certainly not allow a New Beira and a New Algarve in the same longitude as a New Spain, unless one of them for some reason decided to not settle in those lands, and the Iberian Union still happened, and the other was allowed to settle in. Based on the rather aggressive expansion of those two governments in the Americas, I think that this is hard to believe.
The name of the Portuguese possessions would likely have something to do with religion or the local geography, instead of following a “New [insert place]” naming convention. More local placenames would be likely borrowed from the local languages, and then butchered into fitting Portuguese phonology.
Portugal and Spain would have never even started the treaty if they didn’t already suspect the existence of South America. Spain particularly would have absolutely not had it. If anything, it’s Africa that would look more like a splintered mess. So trying to go about the shape of the world by that standard is probably the wrong idea.
They likely would - both treaties are predated by one from 1479, signed in Alcáçovas at the end of the War of Castilian Succession, that already split the Atlantic Ocean and overseas territories between both crowns. Back then the issue was Africa and the Canary Islands. As such, even if South America didn’t exist, both crowns would be bickering for control over something else. Perhaps New Guinea or Australia.
What could change however is where the lines would be split, specially the one for the Treaty of Zaragoza. If ToT was at 82°W (New Zealand Catalonia in this map - roughly halfway between Hispaniola* and Cape Verde, like in the RL ToT), then ToZ would be probably 118°E, roughly at the Indus River. If anything the Portuguese crown would be the ones slightly pissed by this division, as it wanted control over India.
EDIT: in other words I’m not convinced that we should automatically brush off ToT as not happening in that alternate world. Or that Africa would look like [ipsis digitis] a splintered mess.
*present in this map, near Japan.
