"The Yellow Wallpaper" Absolute Control

Charlotte Perkins Gilman's short story "The Yellow Wallpaper" holds many ambiguous themes, however, one of the most intruiging is the theory that the woman in the bedroom is completely insane. While the story holds many instances when it seems as if sanity is intact, for example when her husband comes to vivist the room, the majority of the story revolves around her solitude, which allows for her her mind to be exposed through the narrorator. One of the most interesting examples that contribute to the idea of her complete insanity is the mention of multiple names. While the woman in the room herself is nameless, there are three other women mentioned. Jennie is mentioned as being Johns sister, a woman named Mary who takes care of the baby, and then most interestingly at the end, a woman named Jane mentioned. Jane has no actual role in the story, but acts as something so pause on. My question is, has the woman become this woman named Jane? Or is Jane the woman she has seen in the wallpaper? The woman says "I've got out at last,"... "in spite of you and Jane. And I've pulled off most of the paper, so you can't put me back!". To me this suggests that Jane is the woman she has seen inside the wallpaper, and that she has felt trapped by her, and this is why she felt she needed to tear it down. By tearing down the wallpaper she frees herself spiting Jane and spiting her husband. Although she does this act and is somewhat "freed", I believe that the woman at this point has receded into her own mind. Maybe this is her freedom, because her mind is the only place she can have absolute control.