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Brisbane is named after Sir Thomas Brisbane, who was a governor of New South Wales. The name is English and Scottish and is said to mean "break bone", presumably a name given to a violent person.
Melbourne, I'm sure, is named after William Lamb, Viscount Melbourne, a British Prime Minister of Queen Victoria's reign. The title Viscount Melbourne is now extict. There is an English surname Melbourn(e), from Melbourn in Derbyshire. The name means "mill stream".
I don't think either name is prominent or common today.