The White Wizard was the formal Chief of the Heren Istarion.The title was at first held by Saruman before he took the epiteth of many Colours. After his return the title was taken over by Gandalf, the Order's new head.
Melian was not known as the White Wizard, but she served in the same role when she led the other five wizards as Guardians of the Elves in the Years of the Trees. After their role to escort the willing elves had been fulfilled, she stayed in Middle-earth as Queen of Doriath, while the others who accompanied her would later form the Order of the Istari under Saruman in later Ages.