This is actually a group of lorikeets - many of which look quite similiar.
They are in the genus Trichoglossus and some are subspecies of the genus and species Trichoglossus haematodus
There have been several changes as to whether Lorikeets in Trichglossus are actually their own species or subspecies to T.haematodus. This may continue to change.
Two of the most commonly referred to a Rainbow Lorikeet are the Green-naped Lorikeet and the Swainson's Lorikeet but several others may go under the name