Even though prosperous is the meaning given for
Mira in this database, I do not know the Sanskrit word it is referring to. It certainly was the name of a very famous singer-devotee, but whether her name was of Sanskrit origin (mIra meaning ocean or boundary does exist in Sanskrit) or from Persian root mIr meaning main I cannot say.
I would be interested in finding out the etymology of mIrA meaning prosperous, or at least any use of the word in that sense.