The cat I saw sleeping at the end of my garden earlier this month has definitely made it her home.
She sleeps in a pile of leaves most nights and I've been putting food out for her. Although she eats, it she runs off when I approach and doesn't come back until I have walked away. The fact that she is so timid around humans makes me think she might have been mistreated by her former owners.
She isn't shy around animals. I saw her having a fight with one of my existing cats a couple of days ago and she definitely stood her ground.
I am calling her Luna, because of a comment left on my blog that she has a face like a moon - and I agree that she does. However, I'm not yet quite sure what sex the cat is, so if "she" turns out to be "he" I guess I'll have to think of another name.