Primrose Gardner born in FO 14 (SR 1435) and was the ninth child and fifth daughter of Samwise Gamgee and his beloved wife Rosie Cotton. She had four younger siblings. She was the second child of Sam's not to have a namesake (her sister Elanor being the first), but they perhaps could've gotten the name from her mother Rose. This might've been confusing around the household with both a mother and a sister named Rose, which could be easily mistaken for Primrose.
Primrose is the name of a flower native to western and southern Europe. Naming her 'Primrose' was no doubt keeping with the tradition of hobbits to name the females of their race after that of flowers.