The island of Cyprus most likely got its name from the plant you refer to, i.e., the henna shrub which is plentiful in the island. The plant is known as "Kypros" or "kypeiros" in classical Greek.
Cyprian is related with Cyprus via the name "Kypris" or "Cypris" (meaning "from Cyprus") which was one of Aphrodite's names. When Cronus castrated his dad's (Uranus) doodads and threw them in the sea at his mom's (Gaea) request, the Goddess of LoveAphrodite emerged from the froth by the shores of Paphos, Cyprus. Hence, Cypris. But I digress.