I think the following would be three plausible ways how the landmasses got their names.

1. We have this vague idea that there once was an influential Austral speaking empire. It could have named the different landmasses, which then would have evolved into the names that we will come up with now.

2. At some point there could have been a conference between Austral speaking nations to agree on common names.

3. A resolution in the World Forum (or equivalent) to adopt names for its internal use (that we conveniently also use).

Personally I like number 3.

In all cases, names could have been borrowed from other languages, be references to important people or geographical descriptions. Austral (English) is the lingua franca, and any name should be pronounceable in English (not saying that the suggestions so far aren't, but we shouldn't for example copy/paste the Sedunnic names ).

Sedunn, of course, will retain its own names for its internal use.

Oh, and we should name the oceans and other important stuff too while we are at it!