I was looking up the name a few nights ago, and I found that it was indeed of Persian origin. The site I was looking on, which escapes me now, had it listed as meaning beautiful or pure.
It is derived from the Persian root/word vashta, meaning good or beautiful. It is unique in the sense that it is one of the few proper names in the Tanakh to begin with the letter "waw."
Vashti Bunyan (b 1945) is an English singer-songwriter. Her first album, Just Another Diamond Day, has been extremely influential since its release in 1970.
There's something about this name that I really like, though I can't put my finger on what it is. For some reason, when I hear it, I picture a red-haired seamstress. The seamstress part could be due to it's meaning, but I don't know about the red hair.
"The Complete Book of Muslim and Parsi Names" by Maneka Gandhi and Ozair Husain lists Washti as a Persian name meaning "beauty; goodness", and writes that it is associated with the story of Esther. I assume that Washti is the Persian form of Vashti.
-- Anonymous User 7/6/2012
In the 1956 film "Giant" starring Elizabeth Taylor and Rock Hudson, a rural Texan character is named Vashti. In the film it was pronounced "VASH-tye".