According to Wikipedia:
Kittlaus named Siri after a co-worker in Norway; the name is a short form of the name Sigrid, from Old Norse Sigríðr, composed of the elements sigr "victory" and fríðr "beautiful".
the s in siri stands for stanford and i just wanted to let you know that
edit: not really. but here’s the explanation.
Apple didn’t invent Siri - originally it was made by a company called Siri Inc., which spun out of an organization called SRI, which used to stand for Stanford Research Institute.