Yes I do this too, mostly I tend to associate people with animals. Like if a person has bird-like qualities to their facial features, then I think something like "bird woman." Or maybe remind me of a rabbit, or a cat, a pig, a beaver, a fish, a bear, a horse, whatever. Bear-guy, cat-woman, fish-face, horse-face.
I also notice my cats remind me of different animals, one is reminds me of a bat, one is like a squirrel, one reminds me of a dolphin, another is like a possum, one I call my "little rat." And one of my cats is definitely, to quote btbbnyr, a "rabbit in cat's clothing."