From the State Library of Western Australia website:
The old State Library building had become inadequate and crowded and by the 1970s the building could not hold all the collections and staff and a series of out buildings and annexes were used. As a new building was needed, planning for the new Library began in earnest at the end of 1977 with the appointment of the Perth architects Cameron, Chisholm and Nicol, who worked in association with the Building Management Authority and consulting engineers Norman, Disney and Young Pty Ltd.
Construction of the main library frame began in January 1982. The building was completed early in 1985 and library staff began to move in from the ten different premises and annexes around the city. The building is named after Professor Fred Alexander, Chairman of the Library Board from 1952-1982. The Battye Library and State Archives were housed on the 3rd and 4th floors of the new building. The building opened to the public on 29 April 1985, but the official opening, by then Premier Brian Burke, came on 18 June 1985.
Professor Emeritus Fred Alexander, CBE
The building celebrates the contribution of Professor Emeritus Fred Alexander, CBE, Fellow of the Library Board of Western Australia. Professor Alexander was Chairman of the Board from 1952-1982 and he masterminded the strategies the library service adopted in gaining acceptance of the provision of the 1951 Library Board Act by local authorities throughout the State. Professor Alexander was a policy-maker of wisdom and integrity, who showed his respect for the library profession by leaving professional judgements to the librarians, while he concerned himself with policy direction.
Link to obituary: Academy of the Social Sciences in Australia.