Since this is a case of different dialects, I would be faithful to the spelling in the original. If I were writing in American English I would not change anything about Australian Centre for Astrobiology.
The fourth Q&A in the link provided by @Tim Romano deals specifically with how to handle official names.
Q. My job entails editing and Americanizing books from the UK. We normally change British spellings to American for our audience, like defence to defense or centre to center. But what do I do in cases where one of these words is part of an official name, as in Ministry of Defence? or such-and-such Centre? If I leave the British spelling, it looks wrong compared to the text, but if I change it to the American spelling, it is wrong according to the organization.
A. Don’t worry—neither will look wrong. The text will look American and the name will look British. You can’t change the names of organizations, and most readers will know that.
Granted you've not stated you are editing texts, but you did mention formal writing. But even when texts are being "Americanized," official names are used and not changed.
The third Q&A also appears insightful and applicable to what you have asked about:
Q. I am a translator and in my work I always have to deal with proper names of works of art, locations, streets, cities, etc. What is the rule of thumb for that? Leave in the original language or translate into English? I have seen both. Would you kindly help me?
A. I’m afraid there’s no easy answer, because the decision depends on what you believe will be most useful to the readers you expect to read that work. If you’re translating a scholarly text for specialists, readers will want the original. If you’re translating a spy novel, they won’t necessarily. Sometimes you’ll want both to appear right there in the text (one in parentheses); other times you’ll want to hide one or the other in a note. It’s a decision that should be made with the author’s input, if possible.