Mentha diemenica is known by the common name of slender mint. The species is named after Van Diemen's Land, which is now called Tasmania. It is a mint species within the genus "Mentha", native not only to Tasmania but also to Queensland, New South Wales, Victoria, and South Australia.
Van Diemen's Land is a name older than the name Tasmania.
Considering the context says "Van Diemen's Land, which is now called Tasmania," it can be inferred that the name Tasmania came after the name Van Diemen's Land.