just to point out the bottleneck in the article, IFAIK "Supreme Court of Florida" has no authority changing her name while she has russian citizenship and has a russian passport.
Of course she could just use an artist name, like some
call themselves Lady Gaga or Madonna... but obviously USTA/ITF wouldnt allow that for simply commercial reasons. She needs an official namechange to force USTA/ITF accepting the change. But again, I dont know what "Supreme Court of Florida" can do in this case, especially now she is living in California, i dont know which state gives her green card or residence card...
Long story short, my understanding is she has to change her name in Russia.