Melba is an Australian-English invented name — derived from the city of Melbourne by Dame Nellie Melba, who chose it as her stage surname in 1887 to honor her hometown. Her signature roles were Mimì in La bohème, Marguerite in Faust, and Violetta in La traviata. Two foods are named after her: Peach Melba (Auguste Escoffier created it at the Savoy in London 1892 as a tribute) and Melba toast (also created by Escoffier — thin, twice-baked toast for her ill stomach). Dame Commander of the Order of the British Empire (1918); her face appears on the Australian $100 note.
Melba does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Melba reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.