Knowing the right distances would be extremely important for them. Columbus thought the world map looked like this, which is why he set out on his trip and why almost everyone in Portugal and Spain (rightfully) thought he was an idiot. He got lucky there was an entire continent between Europe and Asia.
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.
America is a continent, composed by North America and South America
United States is a nation from North America
What does this title even mean ? What if Columbus didn't exist ? By the way, if you'd asked yourself why so many African countries spoke French, you wouldn't have drawn your map this way.
EDIT: Oh my, this is bad… Didn’t see that the left part of the map was the current East of Asia.
I owe everyone an apology for my mistake. I will not delete my post as a reminder of my own stupidity.
You'll notice if you look that North America and South America are missing from the map. That's what the title means.
Also, there's no consensus on how many continents there are. Someone from the US would be very surprised to hear that North and South America are the same continent.