A thought or two on the name: Katie could certainly be a diminutive of Katherine, Kathryn, Kathleen, Kathlynn, or any version spelled with a C as well, but it could also be a nickname simply for Kate or a stand alone name.
In Ireland in particular but also most of England, it is common to name a child simply Kate or Katie. Let's not forget that Shakespeare wrote of women name Kate - the name has been popular on its own for quite some time. Although here in the U.S. we saw young girls being named Katie in the past several decades, it was actually a resurgence. According to the SSA, Katie (stand alone name) was one of the top 200 girls names in the country during the 1910s, 1890s, 1880s, etc. Not suggesting that Katie Walker was born in those decades, just that the name was certainly around here and if I'm not mistaken was even more popular in Ireland/England.
Just a couple of thoughts on her well-kept appearance. I've worked with our local homeless population here on the East Coast, and something that has always struck me is that older and elderly homeless women on average seem to be cleaner, more put together, and more "normalized" in appearance than their male counterparts. I think it's a combination of women of that generation having pride in appearance no matter what the circumstances, but also women being more open to receiving assistance and people being less apprehensive about offering help. Statistically it's less likely that an elderly homeless woman is a drug and alcohol abuser or a prostitute, so her lifestyle, although transient, may involve sleeping in group homes from time to time and getting a bed in a shelter with shower facilities when available.
Just some thoughts - my instinct is that if she was a local woman out wandering, someone would have immediately reported her missing, or certainly have done so over the past week. My Grandmother suffered from Alzheimers for nearly a decade, and my Grandpa was her caregiver until one day when I was in college and he had a stroke. During his stroke and the unconsciousness that followed, my Grandma left the house, presumably to seek help. She was lost in a small woods in her own neighborhood for hours, but we were able to get immediate police assistance to locate her because of her condition. Of course, that's assuming that Katie Walker has someone checking up on her every day or few days. A care facility would have been obligated to report immediately, and I would think that an in-home caregiver would as well. Maybe it's possible that she did travel from some distance, or that her inability to recall information happened recently enough that she was mobile and traveling on her own volition.
Poor KW. I hope someone sees this and recognizes her!