"Orchid" is for the flower orchid. From New World Dictionary: "any of a family (Orchidaceae) of perennial plants that grow in the ground as epiphytes and are characterized by a bulbous root system, three petals of which one is lip-shaped with many distinctive forms, waxy pollen masses, and minute seeds." "Orchid" probably suits her beauty and, as a child, her delicate health.
Kaldea's kanji is "ai," which is 9 strokes. The official definition for the English game is "sorrow." "Aware" means "sorrowful, piteous", and "awaremu" means "pity, sympathize." Phrases formed from "ai" include "aiwa" (sad story), "aika" (elegy, lament), and "aishuu" (sadness, sorrow, grief).
"Ai" is fitting for Kaldea. Her tragic past causes her to become a living experiment, and it separates her from her family and her beloved Sion. It also indicates the pity that ties her to Dauragon's side.