The key thing to realize is that each entity involved -- the airline, the two immigration services, and any local agencies like the NHS are each operating independently and trying to verify different things.

When leaving OZ the airline wants to look up your ticket and be sure it's really your ticket so show them the passport with the matching name. They also want to be sure you're eligible to enter the UK. They'll probably be fine with either passport but the Hungarian passport will satisfy them for sure. An EU citizen has the right to live and work in any EU country.

When leaving OZ the Australian immigration service will want to be sure you haven't overstayed your entry permission. It's easiest and best to show them the same passport you entered Australia. If they're concerned (which they won't be if it's an Australian passport) they can match up the entry with the exit and see how long you've been in the country.

When entering the UK show them your Hungarian passport. It doesn't matter that it's different than you've used so far. They'll take one look at the EU symbol, a second look at the picture, and your face, and wave you in. You're eligible to live and work in the UK as an EU citizen. Period.

When you leave the UK the airline will need to be sure you're eligible to enter Australia so they may need to see your Australian passport.

Note that in the above the *only* people who see both passports and/or the name on the ticket and the passport are the airline. And the only reason they care about the name on the passport is to be sure it's not someone else's ticket you purchased. One character differences aren't relevant for that.

Keep in mind that there are passports with names written in non-latin writing systems or in latin transliterations which are not unambiguous. Imagine what a German-Russian dual citizen with a ß in their name has on their Russian passport.... Or a Chinese dual citizen's passport in Thailand... There is an official transliteration to latin characters for the machine-readable portion but who is going to know that when they write their name on a form in a country that doesn't even know what those characters mean?

The bottom line is that "names" are more complex than people realize. People don't necessarily have a single name that's identical everywhere and in every context and a single character is not something to worry about.