I had to modify the original question, but think I was able to preserve its original intent.  The focus of the yellow wallpaper in the story has several specific purposes.  I think that the most pressing of them is that the woman's construction of what is happening in the yellow wallpaper as she studies it from her bed of confinement is the only freedom she is allowed.  She is not allowed to maintain a journal, leave the bedroom, express what she is feeling, or do anything of the sort.  In the end, all she can do is study the wallpaper.  Through this analysis, she projects her own condition of being trapped and subjugated on the designs in the wallpaper.  The importance is to reflect the theme of the role of women and social forms of subjugation that is a part of the experience of being a woman in society.  In showing how the narrator is able to construct and transfer her own reality upon that of the wallpaper, it brings to light that women's voices will have to be heard.  On some level, either society will create forums where this voice can be expressed properly and with a sense of productivity and construction or it will be expressed in a destructive manner.  The story seems to be suggesting that society must make the choice as to how to approach the experience of women in the modern setting.

I believe the main reason the story "The Yellow Walllpaper" is called "The Yellow Wallpaper" is because the story describes a woman suffering from post-partum depression and having a serious breakdown, and she is mostly confined in a room where the wallpaper is a hideous yellow pattern. The woman begins to see the paper as a prison with a woman hidden in the pattern trying to get out. The author, Charlotte Perkins Gilman, describes the color of the paper in great detail, even including that the color comes off onto the narrators clothes when she brushes too close to it. Since the wallpaper is so significant it seems like a separate character, it is understandable that Gilman would point that out in the story's title.