I pronounced it like "Mel-born" until an Australian person corrected me lol. it's like Gloucestershire but in Australia!

Old gen x Australian here, and pretty much everybody I know pronounces it Mel burn.

To pass as local I say the Mel part clearly and mumble bu or bun at random, depending on the mood. So MELBu

But the real test is all the mumbling variations of Straya, AUSTRAia, etc

Is there a similar "tell" with how people pronounce Darwin?

It's ironic Aussies don't pronounce the R in Melbourne considering you add Rs to every other word!