This looks like a "knock down" texture. You can reproduce this by spraying on thinned mud and then knocking down with a knife. Best results are with a sprayer, but you might get by fine with a canned product. Before you do the texture, you should level this out with drywall mud. For info on how to do a knock down and video, see Knock Down Drywall Texture

Check out HD or Lowes. There are aerosol products that will simulate this texture.

Homax Knockdown

Hi' Looks like a thin knock down. Mix up some mud and level out patch, texture won't hide a bad joint or patch. When dry, mix up some mud a little on the wet side then dab it on with plastic bag let it set a bit then knock it down with your blade. If you don't like the result, skim it over and try again.

Good Luck woodbutcher

I agree with geoffrey on the homax. Sand the entire area down to zero texture, then use the homax spray and make it look good. Let that dry, then prime, and paint and your done.

If you have not painted the patch, you can use a damp sponge for smoothing. No dust.