How does everyone do it?
For me, I divide the images in to folders that are like boards, so, I have a lounge folder and a hobby folder and so on.
As for how I name the images, they're named by the site I found them on. For example, if I save two images from Wakachan, I name them "Waka1" and "Waka2". If I'm on Horochan, and I save two images that are related to eachother, I might name them something like "Horo1-1" and "Horo1-2".