What kind of wall/ceiling texture is this?
I don't think there's an actual name for this, maybe grade school art.
After doing all your patching and smoothing out the wall, get a 1&quot; knife, putty knife, dip it in some drywall mud and dap it on the wall. Do it a couple of times without redipping to get the thinner, smaller lines. Dap and twist a bit to get the uneven lines. After it partially dries, you can flatten out a few with the knife to get the smashed down look. Experiment a bit and you'll be surprised how close you can match it. You're lucky, this is an easier pattern to match than most.