Mr M. Lachberg, a member of the Perth Road Board, approached the headmaster of Innaloo State School to conduct a competition among the children to write an essay suggesting names for the local park.
Ken Allen won the competition with his suggestion of the name Birralee. The name is derived from Birralii, meaning child or children in language of the Yuwaalaraay and Gamilaraay people from North-West New South Wales and South-West Queensland. Ken observed that the name would be fitting for a park that would be used by children.
The Perth Road Board proposed the name Birralee Park to the Department of Lands and Surveys in a letter dated 10 March 1959. It was approved and later made official.