'Southern' must surely be related to the Southfarthing;2 it is uncertain whether 'Star' has any particular significance, but it may refer to the five-pointed shape of a pipe-weed flower.
A variety of pipe-weed grown in the Southfarthing of the Shire, and apparently originating in the district around Longbottom. The 'star' of its name presumably refers to the star-shaped flowers of the pipe-weed plant.
Given that Southern Star was only one of several varieties of pipe-weed grown in the Southfarthing, the particular choice of the word 'Southern' may imply that this variety came from the southern parts of that farthing, perhaps even as far south as the regions near Sarn Ford on the Shire's southern border.