Our modern English word "ginger" is spelled
gingifer in Old English from Latin
gingiber. The Latin in turn is from Greek
zingiberis, which is a loan word from Prakrit
singabera (Pali
singiveram) which is from Sanskrit
srngaveram. Although this might be a Sanskrit compound, "horn-body" (
srnga-vera) based on the shape of the ginger root, it's also possible that the Sanskrit word is a Dravidian borrowing (compare the word
inciver, "ginger-root," in Malayalam and Tamil).
The scientific name of the ginger plant is
Zingiber officinale, and Zingiber also provides the genus, family, and order.