Cat’s whiskers seems like a fitting common name for this taxon. Another name is Java tea, which gives hints to both its native distribution (tropical Asia and Queensland) and how it is consumed as a medicine.
Tea made from the leaves of Orthosiphon aristatus, is, at a minimum, a diuretic. The National Parks Board of Singapore summarizes the ethnobotanical uses of Java tea:
It is mainly taken to stimulate urination. According to Indonesian and Malaysian folk medicine, bladder or kidney pain, gout, rheumatism and arteriosclerosis can be treated by drinking a decoction of leaves boiled in water. In Vietnamese folk medicine, a plant infusion is used to treat influenza, hepatits, rheumatism, jaundice and fever, as well as stimulating urination. In India, this plant is used to treat diabetes in combination with the herb Andrographis paniculata.
References associated with some of these claims can be found in the Useful Tropical Plants database: Orthosiphon aristatus.
Orthosiphon means a straight tube (a reference to the united base of the corolla), while aristate is the property of having an awn or beard.