According to Wikipedia, the area is named after Manuka Circle, the street which forms the northern boundary of the precinct. Manuka Circle was on Walter Burley Griffin‘s original plan for Canberra and named after the New Zealand tea tree Leptospermum scoparium.
When Griffin drew up his plans in 1912, there was still some optimism that New Zealand might join the Federation of Australia. Griffin’s plans included eight avenues radiating out from Capital Hill named after the capitals of the six states, the capital of the Northern Territory and the capital of New Zealand.
Before the name Wellington Avenue was gazetted it was realised that New Zealand was not going to become part of a federation of Australasia and the name was replaced by Canberra Avenue.
Griffin planned that the state capital city avenues were terminated with a park named after the generic botanical name for a native plant from that particular site; for example, Telopea Park is named after the waratah, the floral emblem of New South Wales, and is at the end of Sydney Avenue, named after the capital of New South Wales.
So Manuka is a bit of a relic from the original Griffin plan. Why not come and check out this blast from the past by visiting Manuka Arcade!