Well, for one I don't see why the Padanians would have named Australia, and secondly the names of new continents/places/nations aren't consistent, they can be named after the person who discovered them, or a monarch, or a relative of a monarch, or someone who fully explored them for the first time, or just "New *whatever*", or something like "New *whatever*" like "Little Venice" [Venezuela].
Well how about we pick the name of the Italian explorer who discovers SA, and use his, slightly altered, name for the continent.
For Example;
The Medici family started there rise to power in the 1200s, just prior to the time that the southern continent would be discovered, the de'Medicis had brokened into several branches. While somewhat factious, the famaliar ties kept the majority working together. The most powerful was the direct line which had by this time become, basically, the bank and merchant's house of Europe.
Looking to increase profits, the explorer Antonino De'Medici, devised the plan to sail west to the Orient. After gathering five ships and setting out westward he discovered what at first he thought was Mangi, or Southern China. It would not be until his fourth voyage to this land, with further exploration of the coastal regions, that he would come to believe that it was a new land.
The initial news of the discovery of a quicker trade route would cause other people to follow suite. Many of these men, mostly from Italy at first, took to calling these trips Medici Deviazione, or Medici's Detour. As time progressed and others took to using the phrase for the trips, the term became corrupted to what we use today,
Medevia.
That's rather boring, and has probably been done before.
I'd go with some sort of bastardisation of Cipangu.
Below is the etymological progression from Khitan to Cathay as the word travelled westward in OTL:
- Mongolian: Khyatad (Хятад) / Kitad
- Uyghur (Western China): خىتاي, Xitay
- Kazakh: قىتاي, Қытай, Qıtay
- Kazan Tartar (Central Russia): Qıtay
- Russian: Kitay (Китай)
- Bulgarian: Kitay (Китай)
- Latin: Cataya, Kitai
- Spanish: Catay
- Italian: Catai
- Portuguese: Cataio
- English, German, Dutch, Scandinavian: Cathay
Of course we could always go with the term I used above for Southern China, Mangi (also Manji and Manzi)