We call them speckled or spotted eels in NZ but I think they're usually called long-finned eels in Australia (we have an endemic species called the long-finned eel so can't use that name).
Six species of Anguilla have been recorded in Australia. A. megastoma and A. marmorata are both extralimital (apparently known from only one specimen each in Australia, but otherwise widespread in the Pacific region); A. bicolor is only known from the Kimberley region in Australia (widespread elsewhere in the Indian and western Pacific Oceans); A. australis and A. obscura are both uniform in colouration.