No. Not in a civil suit.
Certain criminal acts do provide "Jane Doe" treatment, depending upon the state law.
Remember that BOR filed suit first, before she filed hers. She may have assumed if he had just said "no" (no irony intended) to her out of court settlement proposal, she could have walked away with her privacy still intact. BOR surprised her with his suit against her alleged extortion. So now she unexpectedly has become a publicly known figure.
So she is named as an extortioner?