I believe that it was named after the Australian opera singer Dame Nellie Melba as also was the dessert peach melba .

Yes, it was invented for her, I believe by Antoine Careme, but not sure on the last bit.

All can now be revealed on the Peach Melba!! http://www.theanswerbank.co.uk/Article.go?id=3353

It was indeed named after the Australian soprano Dame Nellie Melba, as was the peach Melba. They were both the creation of Auguste Escoffier, the French chef, in the 1890s when he was the head chef at The Savoy Hotel, London. The toast may well have been a private joke between them. Dame Nellie was a well built, junoesque lady, in the manner of the sopranos of the day, and also possessed of a degree of humour; it is said that Escoffier deliberately had toast sliced in half in response to her enquiry about diet! In his memoirs he described how the peach dish was invented impromptu for her when she returned hungry one evening . What its relation to her toast or her diet was, if any, he did not, I think, tell.